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 <fmiy...@fceia.unr.edu.ar>
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:
<https://antiphishing.vadesecure.com/v4?f=SDlhUlZiaXFEVHROSUhTb0qrO2AR7jfbvbNtVdf1_aC917oIdR0Gc2d8Rd6FD2Bc&i=TFpzSWRVdmRmMGQwa1BoSiimVxxfUPBdU67jVuwVi4s&k=4IV5&r=bzNQRmtWdWVld3VrdkQzNUBU-sIUgBXJ8jKxvWcVsg0fKphq97waH97_kCu1wpxV&s=e2aae9ad20320b735f15a05e15e449b31fb9fc2727a89289de82079d7c61fc15&u=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FExponentially_modified_Gaussian_distribution>.
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
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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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