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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