Eric Thompson wrote:
The supposed example of a Q-Q plot is most certainly not how to make a
Q-Q plot. I don't even know where to start....
First off, the two "Q:s in the title of the plot stand for "quantile",
not "random". The "answer" supplied simply plots two sorted samples of
a distribution against each other. While this may resemble the general
shape of a QQ plot, that is where the similarities end.
The empirical quantiles of a sample are simply the sorted values. You
can plot empirical quantiles of one sample versus some version of
quantiles from a distribution (what qqnorm does) or versus empirical
quantiles of another sample (what Sunil did). The randomness in his
demonstration did two things: it generated some data, and it showed the
variability of the plot under repeated sampling.
Some general advice: be careful who you take advice from on the
internet.
That's good advice.
Duncan Murdoch
The Wikipedia entry for Q-Q plot may be a good start if you
don't know what a Q-Q plot is, although you should also use it with
caution.
Lets say you have some samples that may be normally distributed:
set.seed(1)
x <- rnorm(30)
# now try with R's built in function
qqnorm(x, xlim = c(-3, 3), ylim = c(-3, 3))
# Now try Sunil's "Q-Q plot" method, but for rnorm
# rather than rgamma
some_data <- x
test_data <- rnorm(30)
points(sort(some_data),sort(test_data), col = "blue")
# Note that the points are NOT the same!
This should have been obvious for the simple reason that the QQ plot
should not be influenced by the random number generator that you are
using! A QQ plot is uniquely reproducible. The more general (and
correct) way to get the QQ plot involves choosing a plotting position
and the quantile function (e.g. qnorm or qgamma functions in R) of the
pertinent distribution:
# Sort the data:
x.s <- sort(x)
n <- length(x)
# Plotting position (must be careful here in general!)
p <- ppoints(n)
# Compute the quantile
x.q <- qnorm(p)
points(x.q, x.s, col = "red")
# and they fall exactly on the points generated by qqnorm().
Now, you should be able to generalize this for any distribution. Hope
this helps.
Eric Thompson
2009/9/27 Petar Milin <pmi...@ff.uns.ac.rs>:
Thanks for the answer. Now, only problem is to to get parameter(s) of a
given function. For gamma, I shall try with gammafit() from mhsmm package.
Also, I shall look for others appropriate parameter estimates. Will use
SuppDists too.
Best,
PM
Sunil Suchindran wrote:
#same shape
some_data <- rgamma(500,shape=6,scale=2)
test_data <- rgamma(500,shape=6,scale=2)
plot(sort(some_data),sort(test_data))
# You can also use qqplot(some_data,test_data)
abline(0,1)
# different shape
some_data <- rgamma(500,shape=6,scale=2)
test_data <- rgamma(500,shape=4,scale=2)
plot(sort(some_data),sort(test_data))
abline(0,1)
It is helpful to assess the sampling variability, by
creating repeated sets of test_data, and plotting
all of these along with your observations to create
a confidence "envelope".
The SuppDists provides Inverse Gauss.
On Thu, Sep 17, 2009 at 11:46 AM, Petar Milin <pmi...@ff.uns.ac.rs> wrote:
Hello!
I am trying with this question again:
I would like to test few distributional assumptions for some
behavioral response data. There are few theories about true
distribution of those data, like: normal, lognormal, gamma,
ex-Gaussian (exponential-Gaussian), Wald (inverse Gaussian) etc. The
best way would be via qq-plot, to show to students differences.
First two are trivial:
qqnorm(dat$X)
qqnorm(log(dat$X))
Then, things are getting more "hairy". I am not sure how to make
plots for the rest. I tried gamma with:
qqmath(~ X, data=dat, distribution=function(X)
� qgamma(X, shape, scale))
Which should be the same as:
plot(qgamma(ppoints(dat$X), shape, scale), sort(dat$X))
Shape and scale parameters I got via mhsmm package that has
gammafit() for shape and scale parameters estimation.
Am I on right track? Does anyone know how to plot the rest:
ex-Gaussian (exponential-Gaussian), Wald (inverse Gaussian)?
Thanks,
PM
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