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&i=cFpWc2dOMHdjcFZGMTl4Ng1_zKOb4VfyPb7ITkhLE8Q&k=hNdW&r=bHdDQW5tZDVCemI1ZVczSRLgxDOkCpIXuvcVP3kQ4ZNl3wZFY-aM6EkdaTlJ-T4B&s=a235fcad73b939a4a3e646b9493cfb924ed27ef41d118d10aa17ce462170e545&u=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:
<https://antiphishing.vadesecure.com/v4?f=TzBPM05TMWhaUkVuRncwepXXm7aQUUs8a3sBKnOeo3zqzzPE1PUeJxFSe39wh75Y&i=NmhwUWdPbjljNWRxSlVxNUTscW_rXmsdS5CfW3ms-T8&k=Yhxs&r=bGlzcjBDTTd4VWcyWjZtQ6_TAL2evagZ2vYr-1xJf13LwHIc8EKwrvfWFnwxUdMu&s=54fcca2dabb8b02e9b10abb7c1f2938e90f160a2cb53c8e34c8bf8d215ab3a96&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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