Poisson random number generator
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Hi all please i need to know how to generate a Poisson distributed random variable without using the built-in function (poissrnd).
采纳的回答
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
2012-2-6
1 个投票
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
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
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
PhD Student
2019-7-10
an End is missing
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!
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
Robert
2015-8-14
Thank you for providing this, this is extremely helpful! Does anyone know why the poisrnd function is no longer in MatLab?
John D'Errico
2019-7-10
Because the function name is spelled poissrnd, not poisrnd.
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
Richard Willey
2012-2-6
0 个投票
Mark Steyvers has written a nice book titled "Computational Statistics with MATLAB" which can be downloaded from
The first chapter has a very good section describing inverse transform sampling which provides everything you need to know.
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;
Ahmed raheem
2012-2-7
2 个评论
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
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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