Re: [Scilab-users] I need a numerial procedure to generate Exponentially Modified Gaussian deviates

2024-04-30 Thread Stéphane Mottelet 

See my post on Discourse:

https://scilab.discourse.group/t/exponentially-modified-gaussian-distribution

S.

On 4/30/24 08:46, Stéphane Mottelet wrote:

Hello,

As I already said, there is no need for using this technique, as an EMG
random variable is the sum of a Gaussian and an exponential. If your CDF
reads as

f = (a/2)*exp((a/2)*((a*σ^2)-2*h)) .* erfc((a*σ^2-h)/σ/sqrt(2))

then the underlying variable is the sum of Gaussian of mean 0, variance
σ^2, and an exponential of rate a. Then, you can simulate n draws of
this variable in Scilab with

grand(n,1,"nor",0,σ) + grand(n,1,"exp",a)

S.

On 4/30/24 01:44, Heinz Nabielek wrote:

Very useful. I had done a similar thing with the EMG, but much more
clumsy
Heinz


On 29.04.2024, at 16:41, Federico Miyara 
wrote:


Heinz,

I don't know if this might be useful. The function I'm attaching
allows to generate random numbers according to any distribution,
either empirical or analytical. The results may be scaled if necessary.

Regards,

Federico Miyara


On 29/4/2024 00:11, Heinz Nabielek wrote:

Colleagues:

bird flight altitude probabilities are given by the exponentially
modified Gaussian distribution EMG f=f(h), in my case

f = (a/2)*exp((a/2)*((a*σ^2)-2*h)) .* erfc((a*σ^2-h)/σ/sqrt(2))

with h=hmeasured-85 in meters, a=1/60m, σ=30m. See:
.

For bird flight Monte-Carlo simulations, I need random deviates
representing this distribution.
Normally, I generate the cumulative function F of f. Then, I
project uniform random numbers U(0,1) on F^-1, the inverse of the
cumulative.

With the EMG, closed solutions are not available and I need a
numerial procedure to generate EMG deviates.
What is the best way to do this?
Best greetings
Heinz
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Re: [Scilab-users] I need a numerial procedure to generate Exponentially Modified Gaussian deviates

2024-04-30 Thread Stéphane Mottelet 

Hello,

As I already said, there is no need for using this technique, as an EMG
random variable is the sum of a Gaussian and an exponential. If your CDF
reads as

f = (a/2)*exp((a/2)*((a*σ^2)-2*h)) .* erfc((a*σ^2-h)/σ/sqrt(2))

then the underlying variable is the sum of Gaussian of mean 0, variance
σ^2, and an exponential of rate a. Then, you can simulate n draws of
this variable in Scilab with

grand(n,1,"nor",0,σ) + grand(n,1,"exp",a)

S.

On 4/30/24 01:44, Heinz Nabielek wrote:

Very useful. I had done a similar thing with the EMG, but much more clumsy
Heinz


On 29.04.2024, at 16:41, Federico Miyara  wrote:


Heinz,

I don't know if this might be useful. The function I'm attaching allows to 
generate random numbers according to any distribution, either empirical or 
analytical. The results may be scaled if necessary.

Regards,

Federico Miyara


On 29/4/2024 00:11, Heinz Nabielek wrote:

Colleagues:

bird flight altitude probabilities are given by the exponentially modified 
Gaussian distribution EMG f=f(h), in my case

f = (a/2)*exp((a/2)*((a*σ^2)-2*h)) .* erfc((a*σ^2-h)/σ/sqrt(2))

with h=hmeasured-85 in meters, a=1/60m, σ=30m. See: 
.

For bird flight Monte-Carlo simulations, I need random deviates representing 
this distribution.
Normally, I generate the cumulative function F of f. Then, I project uniform 
random numbers U(0,1) on F^-1, the inverse of the cumulative.

With the EMG, closed solutions are not available and I need a numerial 
procedure to generate EMG deviates.
What is the best way to do this?
Best greetings
Heinz
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Re: [Scilab-users] I need a numerial procedure to generate Exponentially Modified Gaussian deviates

2024-04-29 Thread Heinz Nabielek 
Very useful. I had done a similar thing with the EMG, but much more clumsy
Heinz

> On 29.04.2024, at 16:41, Federico Miyara  wrote:
>
>
> Heinz,
>
> I don't know if this might be useful. The function I'm attaching allows to 
> generate random numbers according to any distribution, either empirical or 
> analytical. The results may be scaled if necessary.
>
> Regards,
>
> Federico Miyara
>
>
> On 29/4/2024 00:11, Heinz Nabielek wrote:
>> Colleagues:
>>
>> bird flight altitude probabilities are given by the exponentially modified 
>> Gaussian distribution EMG f=f(h), in my case
>>
>> f = (a/2)*exp((a/2)*((a*σ^2)-2*h)) .* erfc((a*σ^2-h)/σ/sqrt(2))
>>
>> with h=hmeasured-85 in meters, a=1/60m, σ=30m. See: 
>> .
>>
>> For bird flight Monte-Carlo simulations, I need random deviates representing 
>> this distribution.
>> Normally, I generate the cumulative function F of f. Then, I project uniform 
>> random numbers U(0,1) on F^-1, the inverse of the cumulative.
>>
>> With the EMG, closed solutions are not available and I need a numerial 
>> procedure to generate EMG deviates.
>> What is the best way to do this?
>> Best greetings
>> Heinz
>> This email and any attachments are intended solely for the use of the 
>> individual or entity to whom it is addressed and may be confidential and/or 
>> privileged.
>>
>> If you are not one of the named recipients or have received this email in 
>> error,
>>
>> (i) you should not read, disclose, or copy it,
>>
>> (ii) please notify sender of your receipt by reply email and delete this 
>> email and all attachments,
>>
>> (iii) Dassault Systèmes does not accept or assume any liability or 
>> responsibility for any use of or reliance on this email.
>>
>>
>> Please be informed that your personal data are processed according to our 
>> data privacy policy as described on our website. Should you have any 
>> questions related to personal data protection, please contact 3DS Data 
>> Protection Officer https://www.3ds.com/privacy-policy/contact/
>>
>>
>>
>>
>>
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function x = rand_weighted(w, N)
   // This function generates N random numbers in the unit 
   // interval according to an empirical statistical 
   // distribution given by vector w
   //
   // Usage:
   //x = rand_weighted(w, N)
   //
   // where
   //x: vector containing random numbers
   //w: vector specifying the statistical distribution 
   //   as the probabilities in equally-wide bins along
   //   the unit interval
   //N: number of random numbers to be created  
   //
   // NOTES: 1) Vector w is a probability function, so sum(w) 
   //   must be equal to 1 
   //2) A simple linear transformation such as 
   //   y = a + x*(b - a)
   //   may be used to get a distribution over the 
   //   interval from a to b
   //3) The number M of bins is arbitrary, but as
   //   an interpolation is performed, as M gets
   //   larger the accusacy improves. Usually M 
   //   depends on the size of the sample data used
   //   to estimate the empirical distribution 
   //
   // 
   // Author: Federico Miyara
   // Date:   2017-02-06
   // 2020-03-12
   // 2023-11-05

   M = length(w);

   // Cumulative probability including 0
   W = cumsum([0,w]);

   // The inverse function of the cumulative probability (obtained by
   // linear interpolation) is obtained for a uniformly distributed set
   // of N random numbers between 0 and 1
   x = interp1(W, [0:M]/M, rand(1,N), "spline");

endfunction


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Re: [Scilab-users] I need a numerial procedure to generate Exponentially Modified Gaussian deviates

2024-04-29 Thread Heinz Nabielek 
On 29.04.2024, at 09:24, Stéphane Mottelet  wrote:
>
> Sorry,
>
> This is just a manifestation of another occurence of the xy problem. You
> told about y (drawing from a given PDF) but the original problem was x :
> drawing a random variable which is the sum of two random variables for
> which we already have  generators. In fact an EMG random variable Z may
> be expressed as Z = X + Y, where X and Y are independent, X is Gaussian
> with mean μ and variance σ2, and Y is exponential of rate λ
> (https://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution).
>
> So you just have to use grand
> (https://help.scilab.org/docs/2024.0.0/en_US/grand.html) to make
> independant draws of X and Y then make the sum afterwards


Marvellous. I should have thought of that myself.
Heinz

Shall we try to repeat it in the DISCOURSE?
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Re: [Scilab-users] I need a numerial procedure to generate Exponentially Modified Gaussian deviates

2024-04-29 Thread Stéphane Mottelet 

Sorry,

This is just a manifestation of another occurence of the xy problem. You
told about y (drawing from a given PDF) but the original problem was x :
drawing a random variable which is the sum of two random variables for
which we already have  generators. In fact an EMG random variable Z may
be expressed as Z = X + Y, where X and Y are independent, X is Gaussian
with mean μ and variance σ2, and Y is exponential of rate λ
(https://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution).

So you just have to use grand
(https://help.scilab.org/docs/2024.0.0/en_US/grand.html) to make
independant draws of X and Y then make the sum afterwards

S.


On 4/29/24 08:53, Stéphane Mottelet wrote:

Hello,

I think that the best method available for this application (you wil
need a massive number of draws) is the rejection method
(https://antiphishing.vadesecure.com/v4?f=UERGdHg5cm1GRGl1YjhpeIZFujPY8-l5ZKAsVrZPIXrBA1YUJSBwS6v_Z_tlJsgh=cFpWc2dOMHdjcFZGMTl4Ng1_zKOb4VfyPb7ITkhLE8Q=hNdW=bHdDQW5tZDVCemI1ZVczSRLgxDOkCpIXuvcVP3kQ4ZNl3wZFY-aM6EkdaTlJ-T4B=a235fcad73b939a4a3e646b9493cfb924ed27ef41d118d10aa17ce462170e545=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FRejection_sampling).
Let us continue this
discussion on Scilab's Discourse...

S.

On 4/29/24 05:11, Heinz Nabielek wrote:

Colleagues:

bird flight altitude probabilities are given by the exponentially
modified Gaussian distribution EMG f=f(h), in my case

f = (a/2)*exp((a/2)*((a*σ^2)-2*h)) .* erfc((a*σ^2-h)/σ/sqrt(2))

with h=hmeasured-85 in meters, a=1/60m, σ=30m. See:
.

For bird flight Monte-Carlo simulations, I need random deviates
representing this distribution.
Normally, I generate the cumulative function F of f. Then, I project
uniform random numbers U(0,1) on F^-1, the inverse of the cumulative.

With the EMG, closed solutions are not available and I need a
numerial procedure to generate EMG deviates.
What is the best way to do this?
Best greetings
Heinz
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--
Stéphane Mottelet
Ingénieur de recherche HDR
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
https://antiphishing.vadesecure.com/v4?f=UERGdHg5cm1GRGl1YjhpeIZFujPY8-l5ZKAsVrZPIXrBA1YUJSBwS6v_Z_tlJsgh=cFpWc2dOMHdjcFZGMTl4Ng1_zKOb4VfyPb7ITkhLE8Q=hNdW=bHdDQW5tZDVCemI1ZVczSRLgxDOkCpIXuvcVP3kQ4ZNl3wZFY-aM6EkdaTlJ-T4B=400c609e5d747f0602b75960a3c07a8b840bb89166c364330d50e830fac92ca5=http%3A%2F%2Fwww.utc.fr%2F~mottelet


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Re: [Scilab-users] I need a numerial procedure to generate Exponentially Modified Gaussian deviates

2024-04-29 Thread Stéphane Mottelet 

Hello,

I think that the best method available for this application (you wil
need a massive number of draws) is the rejection method
(https://en.wikipedia.org/wiki/Rejection_sampling). Let us continue this
discussion on Scilab's Discourse...

S.

On 4/29/24 05:11, Heinz Nabielek wrote:

Colleagues:

bird flight altitude probabilities are given by the exponentially modified 
Gaussian distribution EMG f=f(h), in my case

f = (a/2)*exp((a/2)*((a*σ^2)-2*h)) .* erfc((a*σ^2-h)/σ/sqrt(2))

with h=hmeasured-85 in meters, a=1/60m, σ=30m. See: 
.

For bird flight Monte-Carlo simulations, I need random deviates representing 
this distribution.
Normally, I generate the cumulative function F of f. Then, I project uniform 
random numbers U(0,1) on F^-1, the inverse of the cumulative.

With the EMG, closed solutions are not available and I need a numerial 
procedure to generate EMG deviates.
What is the best way to do this?
Best greetings
Heinz
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--
Stéphane Mottelet
Ingénieur de recherche HDR
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
http://www.utc.fr/~mottelet

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