Poisson random number generator

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Ahmed raheem
Ahmed raheem 2012-2-6
评论： Torsten 2022-1-20
Hi all please i need to know how to generate a Poisson distributed random variable without using the built-in function (poissrnd).

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采纳的回答

Andreas Goser
Andreas Goser 2012-2-6
If this is an acadamic exercise - you can look at the literature refererence
% References:
% [1] Devroye, L. (1986) Non-Uniform Random Variate Generation,
% Springer-Verlag.

更多回答（8 个）

Derek O'Connor
Derek O'Connor 2012-2-6
Dirk Kroese has excellent notes here: http://www.maths.uq.edu.au/~kroese/mccourse.pdf, which are based on his book:
D.P. Kroese, T. Taimre, Z.I. Botev: Handbook of Monte Carlo Methods. John Wiley & Sons, 2011.
His notes and book have lots of Matlab examples.
Derek O'Connor
Derek O'Connor 2012-2-7
I prefer this:
% -------------------------------------------------------------
function S = PoissonSamp(lambda,ns);
% -------------------------------------------------------------
% Generate a random sample S of size ns from the (discrete)
% Poisson distribution with parameter lambda.
% Derek O'Connor, 6 Feb 2012. derekroconnor@eircom.net
%
S = zeros(ns,1);
for i = 1:ns
k=1; produ = 1;
produ = produ*rand;
while produ >= exp(-lambda)
produ = produ*rand;
k = k+1;
end
S(i) = k;
end
Derek O'Connor
Derek O'Connor 2012-5-3
I would like to thank Kang Wook Lee of Berkeley for pointing out an error in the code above. The last line should be S(i) = k-1;
% -------------------------------------------------------------
function S = PoissonSamp(lambda,ns);
% -------------------------------------------------------------
% Generate a random sample S of size ns from the (discrete)
% Poisson distribution with parameter lambda.
% Fixed error: changed S(i) = k; to S(i) = k-1;
% Derek O'Connor, 3 May 2012. derekroconnor@eircom.net
%
S = zeros(ns,1);
for i = 1:ns
k=1; produ = 1;
produ = produ*rand;
while produ >= exp(-lambda)
produ = produ*rand;
k = k+1;
end
S(i) = k-1;
end
  2 个评论
Ian Van Giesen
Ian Van Giesen 2020-6-24
Why was the last line changed? Was it to make the events where probability for 'success' a null event? Sorry in advance for a confusing question, still wrapping my head around this, but many thanks for the code!

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Derek O'Connor
Derek O'Connor 2012-7-24
This is a cleaner fix of PoissonSamp
% -------------------------------------------------------------
function S = PoissonSamp3(lambda,ns);
% -------------------------------------------------------------
% Generate a random sample S of size ns from the (discrete)
% Poisson distribution with parameter lambda.
% Fixed error:
% CHANGED k = 1; produ = 1; produ = produ*rand
% TO k = 0; produ = rand;
% Derek O'Connor, 24 July 2012. derekroconnor@eircom.net
%
S = zeros(ns,1);
for i = 1:ns
k = 0;
produ = rand;
while produ >= exp(-lambda)
produ = produ*rand;
k = k+1;
end
S(i) = k;
end
  3 个评论
显示 1更早的评论
John D'Errico
John D'Errico 2019-7-10
Because the function name is spelled poissrnd, not poisrnd.
Binlin Wu
Binlin Wu 2021-4-1
编辑：Binlin Wu 2021-4-2
Would just like to make some minor changes to accept any array size:
function S = PoissonSamp3(lambda,varargin);
% -------------------------------------------------------------
% Generate a random sample S of size ns from the (discrete)
% Poisson distribution with parameter lambda.
% Fixed error:
% CHANGED k = 1; produ = 1; produ = produ*rand
% TO k = 0; produ = rand;
% Derek O'Connor, 24 July 2012. derekroconnor@eircom.net
%
nn = [varargin{:}];
S = zeros([nn,1]);
for i = 1:numel(S(:))
k = 0;
produ = rand;
while produ >= exp(-lambda)
produ = produ*rand;
k = k+1;
end
S(i) = k;
end

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Richard Willey
Richard Willey 2012-2-6
Mark Steyvers has written a nice book titled "Computational Statistics with MATLAB" which can be downloaded from
http://psiexp.ss.uci.edu/research/teachingP205C/205C.pdf
The first chapter has a very good section describing inverse transform sampling which provides everything you need to know.
Ahmed raheem
Ahmed raheem 2012-2-7
First of all, I'd like to thank you all for your cooperation with me. Based on Dirk Kroese, I wrote the following code to generate the Poisson random variable:
The m-file code:
n=1;
lambda=500;
for i=1:10000
x=rand(1);
a=1;
a=a*x;
if a>=exp(-lambda)
n=n+1;
continue
else
X(i)=n-1;
end
end
  • would you please check it if it's correct or not? i feel it is not correct.
Derek O'Connor
Derek O'Connor 2012-2-7
@Ahmed, you're correct, it is not correct.
The function below is a Matlab translation of Kroese's algorithm. It seems to work ok but needs to be thoroughly tested. You should do this and let us know the results. Note that Poisson(L) ~ Norm(L,L), for large L.
The one thing I don't like about Kroese is his awful algorithm and programming style. Why does he use GOTOs instead of proper WHILEs etc?
% -------------------------------------------------------------
function X = Poisson(lambda);
% -------------------------------------------------------------
% Generate a random value from the (discrete) Poisson
% distribution with parameter lambda.
% Derek O'Connor, 6 Feb 2012. derekroconnor@eircom.net
%
k=1; produ = 1;
produ = produ*rand;
while produ >= exp(-lambda)
produ = produ*rand;
k = k+1;
end
X = k;
  1 个评论
Ahmed raheem
Ahmed raheem 2012-2-7
thank you Derek.
it is performing well now...
i putted the code inside a (for loop) and the result was ok.
thanks again.

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Ahmed raheem
Ahmed raheem 2012-2-7
This is the final code:
% -------------------------------------------------------------
function X = Poisson(lambda,n); % n represents the number of iterations
% -------------------------------------------------------------
% Generate a random value from the (discrete) Poisson
% distribution with parameter lambda.
% Derek O'Connor, 6 Feb 2012. derekroconnor@eircom.net
%
for i=1:n;
k=1; usave=1;
usave = usave*rand;
while usave >= exp(-lambda)
usave = usave*rand;
k = k+1;
end
X(i) = k;
end
hist(X)
  2 个评论
Abdulramon Adeyiola
Abdulramon Adeyiola 2022-1-20
@Ahmed raheem I tried using your code to generate 100 samples from Poisson distribution with parameter 1, but the mean of the resulting samples was way above 1. This is strange!
Torsten
Torsten 2022-1-20
L = exp(-lambda);
for i=1:n
k=0; usave=1;
while usave > L
k = k+1;
usave = usave*rand;
end
X(i) = k-1;
end

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