felipecrv commented on code in PR #45058:
URL: https://github.com/apache/arrow/pull/45058#discussion_r1895803198


##########
docs/source/format/StatisticsSchema.rst:
##########
@@ -0,0 +1,883 @@
+.. Licensed to the Apache Software Foundation (ASF) under one
+.. or more contributor license agreements.  See the NOTICE file
+.. distributed with this work for additional information
+.. regarding copyright ownership.  The ASF licenses this file
+.. to you under the Apache License, Version 2.0 (the
+.. "License"); you may not use this file except in compliance
+.. with the License.  You may obtain a copy of the License at
+
+..   http://www.apache.org/licenses/LICENSE-2.0
+
+.. Unless required by applicable law or agreed to in writing,
+.. software distributed under the License is distributed on an
+.. "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+.. KIND, either express or implied.  See the License for the
+.. specific language governing permissions and limitations
+.. under the License.
+
+.. _statistics-schema:
+
+=================
+Statistics schema
+=================
+
+.. warning:: This specification should be considered experimental.
+
+Rationale
+=========
+
+Statistics are useful for fast query processing. Many query engines
+use statistics to optimize their query plan.
+
+Apache Arrow format doesn't have statistics but other formats that can
+be read as Apache Arrow data may have statistics. For example, the
+Apache Parquet C++ implementation can read an Apache Parquet file as
+Apache Arrow data and the Apache Parquet file may have statistics.
+
+We standardize how to represent statistics as an Apache Arrow array
+for easy to exchange.

Review Comment:
   ```suggestion
   We standardize the representation of statistics as an Apache Arrow array
   for ease of exchange.
   ```



##########
docs/source/format/StatisticsSchema.rst:
##########
@@ -0,0 +1,883 @@
+.. Licensed to the Apache Software Foundation (ASF) under one
+.. or more contributor license agreements.  See the NOTICE file
+.. distributed with this work for additional information
+.. regarding copyright ownership.  The ASF licenses this file
+.. to you under the Apache License, Version 2.0 (the
+.. "License"); you may not use this file except in compliance
+.. with the License.  You may obtain a copy of the License at
+
+..   http://www.apache.org/licenses/LICENSE-2.0
+
+.. Unless required by applicable law or agreed to in writing,
+.. software distributed under the License is distributed on an
+.. "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+.. KIND, either express or implied.  See the License for the
+.. specific language governing permissions and limitations
+.. under the License.
+
+.. _statistics-schema:
+
+=================
+Statistics schema
+=================
+
+.. warning:: This specification should be considered experimental.
+
+Rationale
+=========
+
+Statistics are useful for fast query processing. Many query engines
+use statistics to optimize their query plan.
+
+Apache Arrow format doesn't have statistics but other formats that can
+be read as Apache Arrow data may have statistics. For example, the
+Apache Parquet C++ implementation can read an Apache Parquet file as
+Apache Arrow data and the Apache Parquet file may have statistics.
+
+We standardize how to represent statistics as an Apache Arrow array
+for easy to exchange.
+
+Use case
+--------
+
+One of :ref:`c-stream-interface` use cases is the following:
+
+1. Module A reads Apache Parquet file as Apache Arrow data.
+2. Module A passes the read Apache Arrow data to module B through the
+   Arrow C stream interface.
+3. Module B processes the passed Apache Arrow data.
+
+If module A can pass the statistics associated with the Apache Parquet
+file to module B, module B can use the statistics to optimize its
+query plan.
+
+For example, DuckDB uses this approach but DuckDB couldn't use
+statistics because there wasn't the standardized way to represent
+statistics for an Apache Arrow data.
+
+.. seealso::
+
+   `duckdb::ArrowTableFunction::ArrowScanBind() in DuckDB 1.1.3
+   
<https://github.com/duckdb/duckdb/blob/v1.1.3/src/function/table/arrow.cpp#L373-L403>`_
+
+Goals
+-----
+
+* Establish a standard way to represent statistics as an Apache Arrow
+  array.
+
+Non-goals
+---------
+
+* Establish a standard way to pass an Apache Arrow array that
+  represents statistics.
+* Establish a standard way to embed statistics to an Apache Arrow
+  array.
+
+Schema
+======
+
+This specification provides only the schema for statistics. This is
+the canonical schema to represent statistics about an Apache Arrow
+dataset as Apache Arrow data.
+
+Here is the outline of the schema for statistics::
+
+    struct<
+      column: int32,
+      statistics: map<
+        key: dictionary<
+          indices: int32,
+          dictionary: utf8
+        >,
+        items: dense_union<...all needed types...>
+      >
+    >
+
+Here is the details of top-level ``struct``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Name
+     - Data type
+     - Nullable
+     - Notes
+   * - ``column``
+     - ``int32``
+     - ``true``
+     - The zero-based column index, or null if the statistics
+       describe the whole table or record batch.
+
+       The column index is computed as the same rule used by
+       :ref:`ipc-recordbatch-message`.
+   * - ``statistics``
+     - ``map``
+     - ``false``
+     - Statistics for the target column, table or record batch. See
+       the separate table below for details.
+
+Here is the details of the ``map`` of the ``statistics``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Key or items
+     - Data type
+     - Nullable
+     - Notes
+   * - key
+     - ``dictionary<indices: int32, dictionary: utf8>``

Review Comment:
   ```suggestion
        - ``dictionary<values=utf8, indices=int32>``
   ```



##########
docs/source/format/StatisticsSchema.rst:
##########
@@ -0,0 +1,883 @@
+.. Licensed to the Apache Software Foundation (ASF) under one
+.. or more contributor license agreements.  See the NOTICE file
+.. distributed with this work for additional information
+.. regarding copyright ownership.  The ASF licenses this file
+.. to you under the Apache License, Version 2.0 (the
+.. "License"); you may not use this file except in compliance
+.. with the License.  You may obtain a copy of the License at
+
+..   http://www.apache.org/licenses/LICENSE-2.0
+
+.. Unless required by applicable law or agreed to in writing,
+.. software distributed under the License is distributed on an
+.. "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+.. KIND, either express or implied.  See the License for the
+.. specific language governing permissions and limitations
+.. under the License.
+
+.. _statistics-schema:
+
+=================
+Statistics schema
+=================
+
+.. warning:: This specification should be considered experimental.
+
+Rationale
+=========
+
+Statistics are useful for fast query processing. Many query engines
+use statistics to optimize their query plan.
+
+Apache Arrow format doesn't have statistics but other formats that can
+be read as Apache Arrow data may have statistics. For example, the
+Apache Parquet C++ implementation can read an Apache Parquet file as
+Apache Arrow data and the Apache Parquet file may have statistics.
+
+We standardize how to represent statistics as an Apache Arrow array
+for easy to exchange.
+
+Use case
+--------
+
+One of :ref:`c-stream-interface` use cases is the following:
+
+1. Module A reads Apache Parquet file as Apache Arrow data.
+2. Module A passes the read Apache Arrow data to module B through the
+   Arrow C stream interface.
+3. Module B processes the passed Apache Arrow data.
+
+If module A can pass the statistics associated with the Apache Parquet
+file to module B, module B can use the statistics to optimize its
+query plan.
+
+For example, DuckDB uses this approach but DuckDB couldn't use
+statistics because there wasn't the standardized way to represent
+statistics for an Apache Arrow data.
+
+.. seealso::
+
+   `duckdb::ArrowTableFunction::ArrowScanBind() in DuckDB 1.1.3
+   
<https://github.com/duckdb/duckdb/blob/v1.1.3/src/function/table/arrow.cpp#L373-L403>`_
+
+Goals
+-----
+
+* Establish a standard way to represent statistics as an Apache Arrow
+  array.
+
+Non-goals
+---------
+
+* Establish a standard way to pass an Apache Arrow array that
+  represents statistics.
+* Establish a standard way to embed statistics to an Apache Arrow
+  array.
+
+Schema
+======
+
+This specification provides only the schema for statistics. This is
+the canonical schema to represent statistics about an Apache Arrow
+dataset as Apache Arrow data.
+
+Here is the outline of the schema for statistics::
+
+    struct<
+      column: int32,
+      statistics: map<
+        key: dictionary<
+          indices: int32,
+          dictionary: utf8
+        >,
+        items: dense_union<...all needed types...>
+      >
+    >
+
+Here is the details of top-level ``struct``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Name
+     - Data type
+     - Nullable
+     - Notes
+   * - ``column``
+     - ``int32``
+     - ``true``
+     - The zero-based column index, or null if the statistics
+       describe the whole table or record batch.
+
+       The column index is computed as the same rule used by
+       :ref:`ipc-recordbatch-message`.
+   * - ``statistics``
+     - ``map``
+     - ``false``
+     - Statistics for the target column, table or record batch. See
+       the separate table below for details.
+
+Here is the details of the ``map`` of the ``statistics``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Key or items
+     - Data type
+     - Nullable
+     - Notes
+   * - key
+     - ``dictionary<indices: int32, dictionary: utf8>``
+     - ``false``
+     - Statistics key is string. Dictionary is used for
+       efficiency. Different keys are assigned for exact value and
+       approximate value. Also see the separate description below for
+       statistics key.
+   * - items
+     - ``dense_union``
+     - ``false``
+     - Statistics value is dense union. It has at least all needed
+       types based on statistics kinds in the keys. For example, you
+       need at least ``int64`` and ``float64`` types when you have a
+       ``int64`` distinct count statistic and a ``float64`` average
+       byte width statistic. Also see the separate description below
+       for statistics key.

Review Comment:
   ```suggestion
          byte width statistic. See the description of each statistic below.
   ```



##########
docs/source/format/StatisticsSchema.rst:
##########
@@ -0,0 +1,883 @@
+.. Licensed to the Apache Software Foundation (ASF) under one
+.. or more contributor license agreements.  See the NOTICE file
+.. distributed with this work for additional information
+.. regarding copyright ownership.  The ASF licenses this file
+.. to you under the Apache License, Version 2.0 (the
+.. "License"); you may not use this file except in compliance
+.. with the License.  You may obtain a copy of the License at
+
+..   http://www.apache.org/licenses/LICENSE-2.0
+
+.. Unless required by applicable law or agreed to in writing,
+.. software distributed under the License is distributed on an
+.. "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+.. KIND, either express or implied.  See the License for the
+.. specific language governing permissions and limitations
+.. under the License.
+
+.. _statistics-schema:
+
+=================
+Statistics schema
+=================
+
+.. warning:: This specification should be considered experimental.
+
+Rationale
+=========
+
+Statistics are useful for fast query processing. Many query engines
+use statistics to optimize their query plan.
+
+Apache Arrow format doesn't have statistics but other formats that can
+be read as Apache Arrow data may have statistics. For example, the
+Apache Parquet C++ implementation can read an Apache Parquet file as
+Apache Arrow data and the Apache Parquet file may have statistics.
+
+We standardize how to represent statistics as an Apache Arrow array
+for easy to exchange.
+
+Use case
+--------
+
+One of :ref:`c-stream-interface` use cases is the following:
+
+1. Module A reads Apache Parquet file as Apache Arrow data.
+2. Module A passes the read Apache Arrow data to module B through the
+   Arrow C stream interface.
+3. Module B processes the passed Apache Arrow data.
+
+If module A can pass the statistics associated with the Apache Parquet
+file to module B, module B can use the statistics to optimize its
+query plan.
+
+For example, DuckDB uses this approach but DuckDB couldn't use
+statistics because there wasn't the standardized way to represent
+statistics for an Apache Arrow data.
+
+.. seealso::
+
+   `duckdb::ArrowTableFunction::ArrowScanBind() in DuckDB 1.1.3
+   
<https://github.com/duckdb/duckdb/blob/v1.1.3/src/function/table/arrow.cpp#L373-L403>`_
+
+Goals
+-----
+
+* Establish a standard way to represent statistics as an Apache Arrow
+  array.
+
+Non-goals
+---------
+
+* Establish a standard way to pass an Apache Arrow array that
+  represents statistics.
+* Establish a standard way to embed statistics to an Apache Arrow
+  array.
+
+Schema
+======
+
+This specification provides only the schema for statistics. This is
+the canonical schema to represent statistics about an Apache Arrow
+dataset as Apache Arrow data.
+
+Here is the outline of the schema for statistics::
+
+    struct<
+      column: int32,
+      statistics: map<
+        key: dictionary<
+          indices: int32,
+          dictionary: utf8
+        >,

Review Comment:
   I think this will be more clear way of describing the key type:
   
   ```suggestion
           key: dictionary<values=utf8, indices=int32>,
   ```
   
   Given the string representation of this type as defined (by code) here 
https://github.com/apache/arrow/blob/main/cpp/src/arrow/type.cc#L1580



##########
docs/source/format/StatisticsSchema.rst:
##########
@@ -0,0 +1,600 @@
+.. Licensed to the Apache Software Foundation (ASF) under one
+.. or more contributor license agreements.  See the NOTICE file
+.. distributed with this work for additional information
+.. regarding copyright ownership.  The ASF licenses this file
+.. to you under the Apache License, Version 2.0 (the
+.. "License"); you may not use this file except in compliance
+.. with the License.  You may obtain a copy of the License at
+
+..   http://www.apache.org/licenses/LICENSE-2.0
+
+.. Unless required by applicable law or agreed to in writing,
+.. software distributed under the License is distributed on an
+.. "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+.. KIND, either express or implied.  See the License for the
+.. specific language governing permissions and limitations
+.. under the License.
+
+.. _statistics-schema:
+
+=================
+Statistics schema
+=================
+
+.. warning:: This specification should be considered experimental.
+
+Rationale
+=========
+
+Statistics are useful for fast query processing. Many query engines
+use statistics to optimize their query plan.
+
+Apache Arrow format doesn't have statistics but other formats that can
+be read as Apache Arrow data may have statistics. For example, the
+Apache Parquet C++ implementation can read an Apache Parquet file as
+Apache Arrow data and the Apache Parquet file may have statistics.
+
+We standardize how to represent statistics as an Apache Arrow array
+for easy to exchange.
+
+Use case
+--------
+
+One of :ref:`c-stream-interface` use cases is the following:
+
+1. Module A reads Apache Parquet file as Apache Arrow data.
+2. Module A passes the read Apache Arrow data to module B through the
+   Arrow C stream interface.
+3. Module B processes the passed Apache Arrow data.
+
+If module A can pass the statistics associated with the Apache Parquet
+file to module B, module B can use the statistics to optimize its
+query plan.
+
+For example, DuckDB uses this approach but DuckDB couldn't use
+statistics because there wasn't the standardized way to represent
+statistics for an Apache Arrow data.
+
+.. seealso::
+
+   `duckdb::ArrowTableFunction::ArrowScanBind() in DuckDB 1.1.3
+   
<https://github.com/duckdb/duckdb/blob/v1.1.3/src/function/table/arrow.cpp#L373-L403>`_
+
+Goals
+-----
+
+* Establish a standard way to represent statistics as an Apache Arrow
+  array.
+
+Non-goals
+---------
+
+* Establish a standard way to pass an Apache Arrow array that
+  represents statistics.
+* Establish a standard way to embed statistics to an Apache Arrow
+  array.
+
+Schema
+======
+
+This specification provides only the schema for statistics. This is
+the canonical schema to represent statistics about an Apache Arrow
+dataset as Apache Arrow data.
+
+Here is the outline of the schema for statistics::
+
+    struct<
+      column: int32,
+      statistics: map<
+        key: dictionary<
+          indices: int32,
+          dictionary: utf8
+        >,
+        items: dense_union<...all needed types...>
+      >
+    >
+
+Here is the details of top-level ``struct``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Name
+     - Data type
+     - Nullable
+     - Notes
+   * - ``column``
+     - ``int32``
+     - ``true``
+     - The zero-based column index, or null if the statistics
+       describe the whole table or record batch.
+
+       The column index is computed as the same rule used by
+       :ref:`ipc-recordbatch-message`.
+   * - ``statistics``
+     - ``map``
+     - ``false``
+     - Statistics for the target column, table or record batch. See
+       the separate table below for details.
+
+Here is the details of the ``map`` of the ``statistics``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Key or items
+     - Data type
+     - Nullable
+     - Notes
+   * - key
+     - ``dictionary<indices: int32, dictionary: utf8>``

Review Comment:
   @paleolimbot it's hard to shoehorn auxiliary data to the existing protocols. 
By using Arrow Arrays themselves to push statistics we at least don't have to 
introduce another serialization format (like protobuf, JSON [how this proposal 
started], more flatbuffers...).



##########
docs/source/format/StatisticsSchema.rst:
##########
@@ -0,0 +1,883 @@
+.. Licensed to the Apache Software Foundation (ASF) under one
+.. or more contributor license agreements.  See the NOTICE file
+.. distributed with this work for additional information
+.. regarding copyright ownership.  The ASF licenses this file
+.. to you under the Apache License, Version 2.0 (the
+.. "License"); you may not use this file except in compliance
+.. with the License.  You may obtain a copy of the License at
+
+..   http://www.apache.org/licenses/LICENSE-2.0
+
+.. Unless required by applicable law or agreed to in writing,
+.. software distributed under the License is distributed on an
+.. "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+.. KIND, either express or implied.  See the License for the
+.. specific language governing permissions and limitations
+.. under the License.
+
+.. _statistics-schema:
+
+=================
+Statistics schema
+=================
+
+.. warning:: This specification should be considered experimental.
+
+Rationale
+=========
+
+Statistics are useful for fast query processing. Many query engines
+use statistics to optimize their query plan.
+
+Apache Arrow format doesn't have statistics but other formats that can
+be read as Apache Arrow data may have statistics. For example, the
+Apache Parquet C++ implementation can read an Apache Parquet file as
+Apache Arrow data and the Apache Parquet file may have statistics.
+
+We standardize how to represent statistics as an Apache Arrow array
+for easy to exchange.
+
+Use case
+--------
+
+One of :ref:`c-stream-interface` use cases is the following:
+
+1. Module A reads Apache Parquet file as Apache Arrow data.
+2. Module A passes the read Apache Arrow data to module B through the
+   Arrow C stream interface.
+3. Module B processes the passed Apache Arrow data.
+
+If module A can pass the statistics associated with the Apache Parquet
+file to module B, module B can use the statistics to optimize its
+query plan.
+
+For example, DuckDB uses this approach but DuckDB couldn't use
+statistics because there wasn't the standardized way to represent
+statistics for an Apache Arrow data.

Review Comment:
   ```suggestion
   statistics because there wasn't a standardized way to represent
   statistics for the Apache Arrow data.
   ```



##########
docs/source/format/StatisticsSchema.rst:
##########
@@ -0,0 +1,883 @@
+.. Licensed to the Apache Software Foundation (ASF) under one
+.. or more contributor license agreements.  See the NOTICE file
+.. distributed with this work for additional information
+.. regarding copyright ownership.  The ASF licenses this file
+.. to you under the Apache License, Version 2.0 (the
+.. "License"); you may not use this file except in compliance
+.. with the License.  You may obtain a copy of the License at
+
+..   http://www.apache.org/licenses/LICENSE-2.0
+
+.. Unless required by applicable law or agreed to in writing,
+.. software distributed under the License is distributed on an
+.. "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+.. KIND, either express or implied.  See the License for the
+.. specific language governing permissions and limitations
+.. under the License.
+
+.. _statistics-schema:
+
+=================
+Statistics schema
+=================
+
+.. warning:: This specification should be considered experimental.
+
+Rationale
+=========
+
+Statistics are useful for fast query processing. Many query engines
+use statistics to optimize their query plan.
+
+Apache Arrow format doesn't have statistics but other formats that can
+be read as Apache Arrow data may have statistics. For example, the
+Apache Parquet C++ implementation can read an Apache Parquet file as
+Apache Arrow data and the Apache Parquet file may have statistics.
+
+We standardize how to represent statistics as an Apache Arrow array
+for easy to exchange.
+
+Use case
+--------
+
+One of :ref:`c-stream-interface` use cases is the following:
+
+1. Module A reads Apache Parquet file as Apache Arrow data.
+2. Module A passes the read Apache Arrow data to module B through the
+   Arrow C stream interface.
+3. Module B processes the passed Apache Arrow data.
+
+If module A can pass the statistics associated with the Apache Parquet
+file to module B, module B can use the statistics to optimize its
+query plan.
+
+For example, DuckDB uses this approach but DuckDB couldn't use
+statistics because there wasn't the standardized way to represent
+statistics for an Apache Arrow data.
+
+.. seealso::
+
+   `duckdb::ArrowTableFunction::ArrowScanBind() in DuckDB 1.1.3
+   
<https://github.com/duckdb/duckdb/blob/v1.1.3/src/function/table/arrow.cpp#L373-L403>`_
+
+Goals
+-----
+
+* Establish a standard way to represent statistics as an Apache Arrow
+  array.
+
+Non-goals
+---------
+
+* Establish a standard way to pass an Apache Arrow array that
+  represents statistics.
+* Establish a standard way to embed statistics to an Apache Arrow
+  array.

Review Comment:
   ```suggestion
   * Establish a standard way to embed statistics into an Apache Arrow
     array itself.
   ```



##########
docs/source/format/StatisticsSchema.rst:
##########
@@ -0,0 +1,883 @@
+.. Licensed to the Apache Software Foundation (ASF) under one
+.. or more contributor license agreements.  See the NOTICE file
+.. distributed with this work for additional information
+.. regarding copyright ownership.  The ASF licenses this file
+.. to you under the Apache License, Version 2.0 (the
+.. "License"); you may not use this file except in compliance
+.. with the License.  You may obtain a copy of the License at
+
+..   http://www.apache.org/licenses/LICENSE-2.0
+
+.. Unless required by applicable law or agreed to in writing,
+.. software distributed under the License is distributed on an
+.. "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+.. KIND, either express or implied.  See the License for the
+.. specific language governing permissions and limitations
+.. under the License.
+
+.. _statistics-schema:
+
+=================
+Statistics schema
+=================
+
+.. warning:: This specification should be considered experimental.
+
+Rationale
+=========
+
+Statistics are useful for fast query processing. Many query engines
+use statistics to optimize their query plan.
+
+Apache Arrow format doesn't have statistics but other formats that can
+be read as Apache Arrow data may have statistics. For example, the
+Apache Parquet C++ implementation can read an Apache Parquet file as
+Apache Arrow data and the Apache Parquet file may have statistics.
+
+We standardize how to represent statistics as an Apache Arrow array
+for easy to exchange.
+
+Use case
+--------
+
+One of :ref:`c-stream-interface` use cases is the following:
+
+1. Module A reads Apache Parquet file as Apache Arrow data.
+2. Module A passes the read Apache Arrow data to module B through the
+   Arrow C stream interface.
+3. Module B processes the passed Apache Arrow data.
+
+If module A can pass the statistics associated with the Apache Parquet
+file to module B, module B can use the statistics to optimize its
+query plan.
+
+For example, DuckDB uses this approach but DuckDB couldn't use
+statistics because there wasn't the standardized way to represent
+statistics for an Apache Arrow data.
+
+.. seealso::
+
+   `duckdb::ArrowTableFunction::ArrowScanBind() in DuckDB 1.1.3
+   
<https://github.com/duckdb/duckdb/blob/v1.1.3/src/function/table/arrow.cpp#L373-L403>`_
+
+Goals
+-----
+
+* Establish a standard way to represent statistics as an Apache Arrow
+  array.
+
+Non-goals
+---------
+
+* Establish a standard way to pass an Apache Arrow array that
+  represents statistics.
+* Establish a standard way to embed statistics to an Apache Arrow
+  array.
+
+Schema
+======
+
+This specification provides only the schema for statistics. This is
+the canonical schema to represent statistics about an Apache Arrow
+dataset as Apache Arrow data.
+
+Here is the outline of the schema for statistics::
+
+    struct<
+      column: int32,
+      statistics: map<
+        key: dictionary<
+          indices: int32,
+          dictionary: utf8
+        >,
+        items: dense_union<...all needed types...>
+      >
+    >
+
+Here is the details of top-level ``struct``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Name
+     - Data type
+     - Nullable
+     - Notes
+   * - ``column``
+     - ``int32``
+     - ``true``
+     - The zero-based column index, or null if the statistics
+       describe the whole table or record batch.
+
+       The column index is computed as the same rule used by
+       :ref:`ipc-recordbatch-message`.
+   * - ``statistics``
+     - ``map``
+     - ``false``
+     - Statistics for the target column, table or record batch. See
+       the separate table below for details.
+
+Here is the details of the ``map`` of the ``statistics``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Key or items
+     - Data type
+     - Nullable
+     - Notes
+   * - key
+     - ``dictionary<indices: int32, dictionary: utf8>``
+     - ``false``
+     - Statistics key is string. Dictionary is used for
+       efficiency. Different keys are assigned for exact value and
+       approximate value. Also see the separate description below for
+       statistics key.
+   * - items
+     - ``dense_union``
+     - ``false``
+     - Statistics value is dense union. It has at least all needed
+       types based on statistics kinds in the keys. For example, you
+       need at least ``int64`` and ``float64`` types when you have a
+       ``int64`` distinct count statistic and a ``float64`` average
+       byte width statistic. Also see the separate description below
+       for statistics key.
+
+       We don't standardize field names for the dense union because we
+       can access to proper field by type code not name. So we can use
+       any valid name for fields.
+
+.. _statistics-schema-key:
+
+Statistics key
+--------------

Review Comment:
   ```suggestion
   Standard statistics
   -------------------
   ```



##########
docs/source/format/StatisticsSchema.rst:
##########
@@ -0,0 +1,883 @@
+.. Licensed to the Apache Software Foundation (ASF) under one
+.. or more contributor license agreements.  See the NOTICE file
+.. distributed with this work for additional information
+.. regarding copyright ownership.  The ASF licenses this file
+.. to you under the Apache License, Version 2.0 (the
+.. "License"); you may not use this file except in compliance
+.. with the License.  You may obtain a copy of the License at
+
+..   http://www.apache.org/licenses/LICENSE-2.0
+
+.. Unless required by applicable law or agreed to in writing,
+.. software distributed under the License is distributed on an
+.. "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+.. KIND, either express or implied.  See the License for the
+.. specific language governing permissions and limitations
+.. under the License.
+
+.. _statistics-schema:
+
+=================
+Statistics schema
+=================
+
+.. warning:: This specification should be considered experimental.
+
+Rationale
+=========
+
+Statistics are useful for fast query processing. Many query engines
+use statistics to optimize their query plan.
+
+Apache Arrow format doesn't have statistics but other formats that can
+be read as Apache Arrow data may have statistics. For example, the
+Apache Parquet C++ implementation can read an Apache Parquet file as
+Apache Arrow data and the Apache Parquet file may have statistics.
+
+We standardize how to represent statistics as an Apache Arrow array
+for easy to exchange.
+
+Use case
+--------
+
+One of :ref:`c-stream-interface` use cases is the following:
+
+1. Module A reads Apache Parquet file as Apache Arrow data.
+2. Module A passes the read Apache Arrow data to module B through the
+   Arrow C stream interface.
+3. Module B processes the passed Apache Arrow data.
+
+If module A can pass the statistics associated with the Apache Parquet
+file to module B, module B can use the statistics to optimize its
+query plan.
+
+For example, DuckDB uses this approach but DuckDB couldn't use
+statistics because there wasn't the standardized way to represent
+statistics for an Apache Arrow data.
+
+.. seealso::
+
+   `duckdb::ArrowTableFunction::ArrowScanBind() in DuckDB 1.1.3
+   
<https://github.com/duckdb/duckdb/blob/v1.1.3/src/function/table/arrow.cpp#L373-L403>`_
+
+Goals
+-----
+
+* Establish a standard way to represent statistics as an Apache Arrow
+  array.
+
+Non-goals
+---------
+
+* Establish a standard way to pass an Apache Arrow array that
+  represents statistics.
+* Establish a standard way to embed statistics to an Apache Arrow
+  array.
+
+Schema
+======
+
+This specification provides only the schema for statistics. This is
+the canonical schema to represent statistics about an Apache Arrow
+dataset as Apache Arrow data.
+
+Here is the outline of the schema for statistics::
+
+    struct<
+      column: int32,
+      statistics: map<
+        key: dictionary<
+          indices: int32,
+          dictionary: utf8
+        >,
+        items: dense_union<...all needed types...>
+      >
+    >
+
+Here is the details of top-level ``struct``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Name
+     - Data type
+     - Nullable
+     - Notes
+   * - ``column``
+     - ``int32``
+     - ``true``
+     - The zero-based column index, or null if the statistics
+       describe the whole table or record batch.
+
+       The column index is computed as the same rule used by
+       :ref:`ipc-recordbatch-message`.
+   * - ``statistics``
+     - ``map``
+     - ``false``
+     - Statistics for the target column, table or record batch. See
+       the separate table below for details.
+
+Here is the details of the ``map`` of the ``statistics``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Key or items
+     - Data type
+     - Nullable
+     - Notes
+   * - key
+     - ``dictionary<indices: int32, dictionary: utf8>``
+     - ``false``
+     - Statistics key is string. Dictionary is used for
+       efficiency. Different keys are assigned for exact value and
+       approximate value. Also see the separate description below for
+       statistics key.
+   * - items
+     - ``dense_union``
+     - ``false``
+     - Statistics value is dense union. It has at least all needed
+       types based on statistics kinds in the keys. For example, you
+       need at least ``int64`` and ``float64`` types when you have a
+       ``int64`` distinct count statistic and a ``float64`` average
+       byte width statistic. Also see the separate description below
+       for statistics key.
+
+       We don't standardize field names for the dense union because we
+       can access to proper field by type code not name. So we can use
+       any valid name for fields.
+
+.. _statistics-schema-key:
+
+Statistics key
+--------------
+
+Statistics key is string. ``dictionary<int32, utf8>`` is used for
+efficiency.
+
+We assign different statistics keys for individual statistics instead
+of using flags. For example, we assign different statistics keys for
+exact value and approximate value.

Review Comment:
   ```suggestion
   We assign different names for variations of the same statistic instead
   of using flags. For example, we assign different statistic names for
   exact and approximate values of the "distinct_count" statistic.
   ```



##########
docs/source/format/StatisticsSchema.rst:
##########
@@ -0,0 +1,883 @@
+.. Licensed to the Apache Software Foundation (ASF) under one
+.. or more contributor license agreements.  See the NOTICE file
+.. distributed with this work for additional information
+.. regarding copyright ownership.  The ASF licenses this file
+.. to you under the Apache License, Version 2.0 (the
+.. "License"); you may not use this file except in compliance
+.. with the License.  You may obtain a copy of the License at
+
+..   http://www.apache.org/licenses/LICENSE-2.0
+
+.. Unless required by applicable law or agreed to in writing,
+.. software distributed under the License is distributed on an
+.. "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+.. KIND, either express or implied.  See the License for the
+.. specific language governing permissions and limitations
+.. under the License.
+
+.. _statistics-schema:
+
+=================
+Statistics schema
+=================
+
+.. warning:: This specification should be considered experimental.
+
+Rationale
+=========
+
+Statistics are useful for fast query processing. Many query engines
+use statistics to optimize their query plan.
+
+Apache Arrow format doesn't have statistics but other formats that can
+be read as Apache Arrow data may have statistics. For example, the
+Apache Parquet C++ implementation can read an Apache Parquet file as
+Apache Arrow data and the Apache Parquet file may have statistics.
+
+We standardize how to represent statistics as an Apache Arrow array
+for easy to exchange.
+
+Use case
+--------
+
+One of :ref:`c-stream-interface` use cases is the following:
+
+1. Module A reads Apache Parquet file as Apache Arrow data.
+2. Module A passes the read Apache Arrow data to module B through the
+   Arrow C stream interface.
+3. Module B processes the passed Apache Arrow data.
+
+If module A can pass the statistics associated with the Apache Parquet
+file to module B, module B can use the statistics to optimize its
+query plan.
+
+For example, DuckDB uses this approach but DuckDB couldn't use
+statistics because there wasn't the standardized way to represent
+statistics for an Apache Arrow data.
+
+.. seealso::
+
+   `duckdb::ArrowTableFunction::ArrowScanBind() in DuckDB 1.1.3
+   
<https://github.com/duckdb/duckdb/blob/v1.1.3/src/function/table/arrow.cpp#L373-L403>`_
+
+Goals
+-----
+
+* Establish a standard way to represent statistics as an Apache Arrow
+  array.
+
+Non-goals
+---------
+
+* Establish a standard way to pass an Apache Arrow array that
+  represents statistics.
+* Establish a standard way to embed statistics to an Apache Arrow
+  array.
+
+Schema
+======
+
+This specification provides only the schema for statistics. This is
+the canonical schema to represent statistics about an Apache Arrow
+dataset as Apache Arrow data.
+
+Here is the outline of the schema for statistics::
+
+    struct<
+      column: int32,
+      statistics: map<
+        key: dictionary<
+          indices: int32,
+          dictionary: utf8
+        >,
+        items: dense_union<...all needed types...>
+      >
+    >
+
+Here is the details of top-level ``struct``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Name
+     - Data type
+     - Nullable
+     - Notes
+   * - ``column``
+     - ``int32``
+     - ``true``
+     - The zero-based column index, or null if the statistics
+       describe the whole table or record batch.
+
+       The column index is computed as the same rule used by
+       :ref:`ipc-recordbatch-message`.
+   * - ``statistics``
+     - ``map``
+     - ``false``
+     - Statistics for the target column, table or record batch. See
+       the separate table below for details.
+
+Here is the details of the ``map`` of the ``statistics``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Key or items
+     - Data type
+     - Nullable
+     - Notes
+   * - key
+     - ``dictionary<indices: int32, dictionary: utf8>``
+     - ``false``
+     - Statistics key is string. Dictionary is used for
+       efficiency. Different keys are assigned for exact value and
+       approximate value. Also see the separate description below for
+       statistics key.

Review Comment:
   ```suggestion
        - The string key is the name of the statistic. Dictionary-encoding is 
used for
          efficiency as the same statistic may be repeated for different 
columns.
          Different keys are assigned for exact and
          approximate statistic values. Each statistic has their own 
description below.
   ```



##########
docs/source/format/StatisticsSchema.rst:
##########
@@ -0,0 +1,883 @@
+.. Licensed to the Apache Software Foundation (ASF) under one
+.. or more contributor license agreements.  See the NOTICE file
+.. distributed with this work for additional information
+.. regarding copyright ownership.  The ASF licenses this file
+.. to you under the Apache License, Version 2.0 (the
+.. "License"); you may not use this file except in compliance
+.. with the License.  You may obtain a copy of the License at
+
+..   http://www.apache.org/licenses/LICENSE-2.0
+
+.. Unless required by applicable law or agreed to in writing,
+.. software distributed under the License is distributed on an
+.. "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+.. KIND, either express or implied.  See the License for the
+.. specific language governing permissions and limitations
+.. under the License.
+
+.. _statistics-schema:
+
+=================
+Statistics schema
+=================
+
+.. warning:: This specification should be considered experimental.
+
+Rationale
+=========
+
+Statistics are useful for fast query processing. Many query engines
+use statistics to optimize their query plan.
+
+Apache Arrow format doesn't have statistics but other formats that can
+be read as Apache Arrow data may have statistics. For example, the
+Apache Parquet C++ implementation can read an Apache Parquet file as
+Apache Arrow data and the Apache Parquet file may have statistics.
+
+We standardize how to represent statistics as an Apache Arrow array
+for easy to exchange.
+
+Use case
+--------
+
+One of :ref:`c-stream-interface` use cases is the following:
+
+1. Module A reads Apache Parquet file as Apache Arrow data.
+2. Module A passes the read Apache Arrow data to module B through the
+   Arrow C stream interface.
+3. Module B processes the passed Apache Arrow data.
+
+If module A can pass the statistics associated with the Apache Parquet
+file to module B, module B can use the statistics to optimize its
+query plan.
+
+For example, DuckDB uses this approach but DuckDB couldn't use
+statistics because there wasn't the standardized way to represent
+statistics for an Apache Arrow data.
+
+.. seealso::
+
+   `duckdb::ArrowTableFunction::ArrowScanBind() in DuckDB 1.1.3
+   
<https://github.com/duckdb/duckdb/blob/v1.1.3/src/function/table/arrow.cpp#L373-L403>`_
+
+Goals
+-----
+
+* Establish a standard way to represent statistics as an Apache Arrow
+  array.
+
+Non-goals
+---------
+
+* Establish a standard way to pass an Apache Arrow array that
+  represents statistics.
+* Establish a standard way to embed statistics to an Apache Arrow
+  array.
+
+Schema
+======
+
+This specification provides only the schema for statistics. This is
+the canonical schema to represent statistics about an Apache Arrow
+dataset as Apache Arrow data.
+
+Here is the outline of the schema for statistics::
+
+    struct<
+      column: int32,
+      statistics: map<
+        key: dictionary<
+          indices: int32,
+          dictionary: utf8
+        >,
+        items: dense_union<...all needed types...>
+      >
+    >
+
+Here is the details of top-level ``struct``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Name
+     - Data type
+     - Nullable
+     - Notes
+   * - ``column``
+     - ``int32``
+     - ``true``
+     - The zero-based column index, or null if the statistics
+       describe the whole table or record batch.
+
+       The column index is computed as the same rule used by
+       :ref:`ipc-recordbatch-message`.
+   * - ``statistics``
+     - ``map``
+     - ``false``
+     - Statistics for the target column, table or record batch. See
+       the separate table below for details.
+
+Here is the details of the ``map`` of the ``statistics``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Key or items
+     - Data type
+     - Nullable
+     - Notes
+   * - key
+     - ``dictionary<indices: int32, dictionary: utf8>``
+     - ``false``
+     - Statistics key is string. Dictionary is used for
+       efficiency. Different keys are assigned for exact value and
+       approximate value. Also see the separate description below for
+       statistics key.
+   * - items
+     - ``dense_union``
+     - ``false``
+     - Statistics value is dense union. It has at least all needed
+       types based on statistics kinds in the keys. For example, you
+       need at least ``int64`` and ``float64`` types when you have a
+       ``int64`` distinct count statistic and a ``float64`` average
+       byte width statistic. Also see the separate description below
+       for statistics key.
+
+       We don't standardize field names for the dense union because we
+       can access to proper field by type code not name. So we can use
+       any valid name for fields.

Review Comment:
   This can be misunderstood as the key name as not everyone knows that unions 
have named alternatives in Arrow.



##########
docs/source/format/StatisticsSchema.rst:
##########
@@ -0,0 +1,883 @@
+.. Licensed to the Apache Software Foundation (ASF) under one
+.. or more contributor license agreements.  See the NOTICE file
+.. distributed with this work for additional information
+.. regarding copyright ownership.  The ASF licenses this file
+.. to you under the Apache License, Version 2.0 (the
+.. "License"); you may not use this file except in compliance
+.. with the License.  You may obtain a copy of the License at
+
+..   http://www.apache.org/licenses/LICENSE-2.0
+
+.. Unless required by applicable law or agreed to in writing,
+.. software distributed under the License is distributed on an
+.. "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+.. KIND, either express or implied.  See the License for the
+.. specific language governing permissions and limitations
+.. under the License.
+
+.. _statistics-schema:
+
+=================
+Statistics schema
+=================
+
+.. warning:: This specification should be considered experimental.
+
+Rationale
+=========
+
+Statistics are useful for fast query processing. Many query engines
+use statistics to optimize their query plan.
+
+Apache Arrow format doesn't have statistics but other formats that can
+be read as Apache Arrow data may have statistics. For example, the
+Apache Parquet C++ implementation can read an Apache Parquet file as
+Apache Arrow data and the Apache Parquet file may have statistics.
+
+We standardize how to represent statistics as an Apache Arrow array
+for easy to exchange.
+
+Use case
+--------
+
+One of :ref:`c-stream-interface` use cases is the following:
+
+1. Module A reads Apache Parquet file as Apache Arrow data.
+2. Module A passes the read Apache Arrow data to module B through the
+   Arrow C stream interface.
+3. Module B processes the passed Apache Arrow data.
+
+If module A can pass the statistics associated with the Apache Parquet
+file to module B, module B can use the statistics to optimize its
+query plan.
+
+For example, DuckDB uses this approach but DuckDB couldn't use
+statistics because there wasn't the standardized way to represent
+statistics for an Apache Arrow data.
+
+.. seealso::
+
+   `duckdb::ArrowTableFunction::ArrowScanBind() in DuckDB 1.1.3
+   
<https://github.com/duckdb/duckdb/blob/v1.1.3/src/function/table/arrow.cpp#L373-L403>`_
+
+Goals
+-----
+
+* Establish a standard way to represent statistics as an Apache Arrow
+  array.
+
+Non-goals
+---------
+
+* Establish a standard way to pass an Apache Arrow array that
+  represents statistics.
+* Establish a standard way to embed statistics to an Apache Arrow
+  array.
+
+Schema
+======
+
+This specification provides only the schema for statistics. This is
+the canonical schema to represent statistics about an Apache Arrow
+dataset as Apache Arrow data.
+
+Here is the outline of the schema for statistics::
+
+    struct<
+      column: int32,
+      statistics: map<
+        key: dictionary<
+          indices: int32,
+          dictionary: utf8
+        >,
+        items: dense_union<...all needed types...>
+      >
+    >
+
+Here is the details of top-level ``struct``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Name
+     - Data type
+     - Nullable
+     - Notes
+   * - ``column``
+     - ``int32``
+     - ``true``
+     - The zero-based column index, or null if the statistics
+       describe the whole table or record batch.
+
+       The column index is computed as the same rule used by
+       :ref:`ipc-recordbatch-message`.
+   * - ``statistics``
+     - ``map``
+     - ``false``
+     - Statistics for the target column, table or record batch. See
+       the separate table below for details.
+
+Here is the details of the ``map`` of the ``statistics``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Key or items
+     - Data type
+     - Nullable
+     - Notes
+   * - key
+     - ``dictionary<indices: int32, dictionary: utf8>``
+     - ``false``
+     - Statistics key is string. Dictionary is used for
+       efficiency. Different keys are assigned for exact value and
+       approximate value. Also see the separate description below for
+       statistics key.
+   * - items
+     - ``dense_union``
+     - ``false``
+     - Statistics value is dense union. It has at least all needed
+       types based on statistics kinds in the keys. For example, you
+       need at least ``int64`` and ``float64`` types when you have a
+       ``int64`` distinct count statistic and a ``float64`` average
+       byte width statistic. Also see the separate description below
+       for statistics key.
+
+       We don't standardize field names for the dense union because we
+       can access to proper field by type code not name. So we can use
+       any valid name for fields.
+
+.. _statistics-schema-key:
+
+Statistics key
+--------------
+
+Statistics key is string. ``dictionary<int32, utf8>`` is used for
+efficiency.
+
+We assign different statistics keys for individual statistics instead
+of using flags. For example, we assign different statistics keys for
+exact value and approximate value.
+
+The colon symbol ``:`` is to be used as a namespace separator like
+:ref:`format_metadata`. It can be used multiple times in a key.
+
+The ``ARROW`` pattern is a reserved namespace for pre-defined
+statistics keys. User-defined statistics must not use it.

Review Comment:
   ```suggestion
   The ``ARROW`` prefix is a reserved namespace for pre-defined
   statistic names in current and future versions of this specification.
   User-defined statistics must not use it.
   ```



##########
docs/source/format/StatisticsSchema.rst:
##########
@@ -0,0 +1,883 @@
+.. Licensed to the Apache Software Foundation (ASF) under one
+.. or more contributor license agreements.  See the NOTICE file
+.. distributed with this work for additional information
+.. regarding copyright ownership.  The ASF licenses this file
+.. to you under the Apache License, Version 2.0 (the
+.. "License"); you may not use this file except in compliance
+.. with the License.  You may obtain a copy of the License at
+
+..   http://www.apache.org/licenses/LICENSE-2.0
+
+.. Unless required by applicable law or agreed to in writing,
+.. software distributed under the License is distributed on an
+.. "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+.. KIND, either express or implied.  See the License for the
+.. specific language governing permissions and limitations
+.. under the License.
+
+.. _statistics-schema:
+
+=================
+Statistics schema
+=================
+
+.. warning:: This specification should be considered experimental.
+
+Rationale
+=========
+
+Statistics are useful for fast query processing. Many query engines
+use statistics to optimize their query plan.
+
+Apache Arrow format doesn't have statistics but other formats that can
+be read as Apache Arrow data may have statistics. For example, the
+Apache Parquet C++ implementation can read an Apache Parquet file as
+Apache Arrow data and the Apache Parquet file may have statistics.
+
+We standardize how to represent statistics as an Apache Arrow array
+for easy to exchange.
+
+Use case
+--------
+
+One of :ref:`c-stream-interface` use cases is the following:
+
+1. Module A reads Apache Parquet file as Apache Arrow data.
+2. Module A passes the read Apache Arrow data to module B through the
+   Arrow C stream interface.
+3. Module B processes the passed Apache Arrow data.
+
+If module A can pass the statistics associated with the Apache Parquet
+file to module B, module B can use the statistics to optimize its
+query plan.
+
+For example, DuckDB uses this approach but DuckDB couldn't use
+statistics because there wasn't the standardized way to represent
+statistics for an Apache Arrow data.
+
+.. seealso::
+
+   `duckdb::ArrowTableFunction::ArrowScanBind() in DuckDB 1.1.3
+   
<https://github.com/duckdb/duckdb/blob/v1.1.3/src/function/table/arrow.cpp#L373-L403>`_
+
+Goals
+-----
+
+* Establish a standard way to represent statistics as an Apache Arrow
+  array.
+
+Non-goals
+---------
+
+* Establish a standard way to pass an Apache Arrow array that
+  represents statistics.
+* Establish a standard way to embed statistics to an Apache Arrow
+  array.
+
+Schema
+======
+
+This specification provides only the schema for statistics. This is
+the canonical schema to represent statistics about an Apache Arrow
+dataset as Apache Arrow data.
+
+Here is the outline of the schema for statistics::
+
+    struct<
+      column: int32,
+      statistics: map<
+        key: dictionary<
+          indices: int32,
+          dictionary: utf8
+        >,
+        items: dense_union<...all needed types...>
+      >
+    >
+
+Here is the details of top-level ``struct``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Name
+     - Data type
+     - Nullable
+     - Notes
+   * - ``column``
+     - ``int32``
+     - ``true``
+     - The zero-based column index, or null if the statistics
+       describe the whole table or record batch.
+
+       The column index is computed as the same rule used by
+       :ref:`ipc-recordbatch-message`.
+   * - ``statistics``
+     - ``map``
+     - ``false``
+     - Statistics for the target column, table or record batch. See
+       the separate table below for details.
+
+Here is the details of the ``map`` of the ``statistics``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Key or items
+     - Data type
+     - Nullable
+     - Notes
+   * - key
+     - ``dictionary<indices: int32, dictionary: utf8>``
+     - ``false``
+     - Statistics key is string. Dictionary is used for
+       efficiency. Different keys are assigned for exact value and
+       approximate value. Also see the separate description below for
+       statistics key.
+   * - items
+     - ``dense_union``
+     - ``false``
+     - Statistics value is dense union. It has at least all needed
+       types based on statistics kinds in the keys. For example, you
+       need at least ``int64`` and ``float64`` types when you have a
+       ``int64`` distinct count statistic and a ``float64`` average
+       byte width statistic. Also see the separate description below
+       for statistics key.
+
+       We don't standardize field names for the dense union because we
+       can access to proper field by type code not name. So we can use
+       any valid name for fields.
+
+.. _statistics-schema-key:
+
+Statistics key
+--------------
+
+Statistics key is string. ``dictionary<int32, utf8>`` is used for
+efficiency.

Review Comment:
   ```suggestion
   Each statistic kind has a name that appears as a key in the statistics map
   for each column or entire table. ``dictionary<values=utf8, indices=int32>``
   is used to encode the key for space-efficiency.
   ```



##########
docs/source/format/StatisticsSchema.rst:
##########
@@ -0,0 +1,883 @@
+.. Licensed to the Apache Software Foundation (ASF) under one
+.. or more contributor license agreements.  See the NOTICE file
+.. distributed with this work for additional information
+.. regarding copyright ownership.  The ASF licenses this file
+.. to you under the Apache License, Version 2.0 (the
+.. "License"); you may not use this file except in compliance
+.. with the License.  You may obtain a copy of the License at
+
+..   http://www.apache.org/licenses/LICENSE-2.0
+
+.. Unless required by applicable law or agreed to in writing,
+.. software distributed under the License is distributed on an
+.. "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+.. KIND, either express or implied.  See the License for the
+.. specific language governing permissions and limitations
+.. under the License.
+
+.. _statistics-schema:
+
+=================
+Statistics schema
+=================
+
+.. warning:: This specification should be considered experimental.
+
+Rationale
+=========
+
+Statistics are useful for fast query processing. Many query engines
+use statistics to optimize their query plan.
+
+Apache Arrow format doesn't have statistics but other formats that can
+be read as Apache Arrow data may have statistics. For example, the
+Apache Parquet C++ implementation can read an Apache Parquet file as
+Apache Arrow data and the Apache Parquet file may have statistics.
+
+We standardize how to represent statistics as an Apache Arrow array
+for easy to exchange.
+
+Use case
+--------
+
+One of :ref:`c-stream-interface` use cases is the following:
+
+1. Module A reads Apache Parquet file as Apache Arrow data.
+2. Module A passes the read Apache Arrow data to module B through the
+   Arrow C stream interface.
+3. Module B processes the passed Apache Arrow data.
+
+If module A can pass the statistics associated with the Apache Parquet
+file to module B, module B can use the statistics to optimize its
+query plan.
+
+For example, DuckDB uses this approach but DuckDB couldn't use
+statistics because there wasn't the standardized way to represent
+statistics for an Apache Arrow data.
+
+.. seealso::
+
+   `duckdb::ArrowTableFunction::ArrowScanBind() in DuckDB 1.1.3
+   
<https://github.com/duckdb/duckdb/blob/v1.1.3/src/function/table/arrow.cpp#L373-L403>`_
+
+Goals
+-----
+
+* Establish a standard way to represent statistics as an Apache Arrow
+  array.
+
+Non-goals
+---------
+
+* Establish a standard way to pass an Apache Arrow array that
+  represents statistics.
+* Establish a standard way to embed statistics to an Apache Arrow
+  array.
+
+Schema
+======
+
+This specification provides only the schema for statistics. This is
+the canonical schema to represent statistics about an Apache Arrow
+dataset as Apache Arrow data.
+
+Here is the outline of the schema for statistics::
+
+    struct<
+      column: int32,
+      statistics: map<
+        key: dictionary<
+          indices: int32,
+          dictionary: utf8
+        >,
+        items: dense_union<...all needed types...>
+      >
+    >
+
+Here is the details of top-level ``struct``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Name
+     - Data type
+     - Nullable
+     - Notes
+   * - ``column``
+     - ``int32``
+     - ``true``
+     - The zero-based column index, or null if the statistics
+       describe the whole table or record batch.
+
+       The column index is computed as the same rule used by
+       :ref:`ipc-recordbatch-message`.
+   * - ``statistics``
+     - ``map``
+     - ``false``
+     - Statistics for the target column, table or record batch. See
+       the separate table below for details.
+
+Here is the details of the ``map`` of the ``statistics``:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Key or items
+     - Data type
+     - Nullable
+     - Notes
+   * - key
+     - ``dictionary<indices: int32, dictionary: utf8>``
+     - ``false``
+     - Statistics key is string. Dictionary is used for
+       efficiency. Different keys are assigned for exact value and
+       approximate value. Also see the separate description below for
+       statistics key.
+   * - items
+     - ``dense_union``
+     - ``false``
+     - Statistics value is dense union. It has at least all needed
+       types based on statistics kinds in the keys. For example, you
+       need at least ``int64`` and ``float64`` types when you have a
+       ``int64`` distinct count statistic and a ``float64`` average
+       byte width statistic. Also see the separate description below
+       for statistics key.
+
+       We don't standardize field names for the dense union because we
+       can access to proper field by type code not name. So we can use
+       any valid name for fields.
+
+.. _statistics-schema-key:
+
+Statistics key
+--------------
+
+Statistics key is string. ``dictionary<int32, utf8>`` is used for
+efficiency.
+
+We assign different statistics keys for individual statistics instead
+of using flags. For example, we assign different statistics keys for
+exact value and approximate value.
+
+The colon symbol ``:`` is to be used as a namespace separator like
+:ref:`format_metadata`. It can be used multiple times in a key.
+
+The ``ARROW`` pattern is a reserved namespace for pre-defined
+statistics keys. User-defined statistics must not use it.
+For example, you can use your product name as namespace
+such as ``MY_PRODUCT:my_statistics:exact``.
+
+Here are pre-defined statistics keys:
+
+.. list-table::
+   :header-rows: 1
+
+   * - Key
+     - Data type
+     - Notes
+   * - ``ARROW:average_byte_width:exact``
+     - ``float64``
+     - The average size in bytes of a row in the target
+       column. (exact)
+   * - ``ARROW:average_byte_width:approximate``
+     - ``float64``
+     - The average size in bytes of a row in the target
+       column. (approximate)
+   * - ``ARROW:distinct_count:exact``
+     - ``int64``
+     - The number of distinct values in the target column. (exact)
+   * - ``ARROW:distinct_count:approximate``
+     - ``float64``
+     - The number of distinct values in the target
+       column. (approximate)
+   * - ``ARROW:max_byte_width:exact``
+     - ``int64``
+     - The maximum size in bytes of a row in the target
+       column. (exact)
+   * - ``ARROW:max_byte_width:approximate``
+     - ``float64``
+     - The maximum size in bytes of a row in the target
+       column. (approximate)
+   * - ``ARROW:max_value:exact``
+     - Target dependent
+     - The maximum value in the target column. (exact)
+   * - ``ARROW:max_value:approximate``
+     - Target dependent
+     - The maximum value in the target column. (approximate)
+   * - ``ARROW:min_value:exact``
+     - Target dependent
+     - The minimum value in the target column. (exact)
+   * - ``ARROW:min_value:approximate``
+     - Target dependent
+     - The minimum value in the target column. (approximate)
+   * - ``ARROW:null_count:exact``
+     - ``int64``
+     - The number of nulls in the target column. (exact)
+   * - ``ARROW:null_count:approximate``
+     - ``float64``
+     - The number of nulls in the target column. (approximate)
+   * - ``ARROW:row_count:exact``
+     - ``int64``
+     - The number of rows in the target table, record batch or
+       array. (exact)
+   * - ``ARROW:row_count:approximate``
+     - ``float64``
+     - The number of rows in the target table, record batch or
+       array. (approximate)
+
+If you find a missing statistics key that is usable for multiple
+systems, please propose it on the `Apache Arrow development
+mailing-list <https://arrow.apache.org/community/>`__.

Review Comment:
   ```suggestion
   If you find a statistic that might be useful to multiple
   systems, please propose it on the `Apache Arrow development
   mailing-list <https://arrow.apache.org/community/>`__.
   
   Interoperability improves when producers and consumers of
   statistics agree on a previously agreed upon statistic
   specification.
   ```



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