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Someone please help me, I have probability mass function as follwing, How can generate 100 random values of j from this probability mass function?

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Note: λ>0 and 0≤α≤1/2 and 0≤P(X=j)≤1. (Take initial valus for λ, α and p(X=j) from thir domain as you like as example)
I want to generate randomly 100 numbers (values for j) with this probability mass function . But I really have no idea how and where to start.
Can somebody help me?
Thank you in advance

Akzeptierte Antwort

Jeff Miller
Jeff Miller am 21 Aug. 2020
If you would like to generate 100 random j values, use the function KSSV gave you to generate the f values for the probability masses (they are not all 0's after the for loop, only before it). Then:
sump = cumsum(f);
r_unif = rand(100,1);
r_j = zeros(100,1);
for i=1:100
r_j(i) = find(sump>r_unif(i),1);

Weitere Antworten (2)

KSSV am 20 Aug. 2020
  1. DEfine alpha and lambda values.
  2. DEfine j value.
  3. WRite your formula and substitute those values.
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Bruno Luong
Bruno Luong am 21 Aug. 2020
Bearbeitet: Bruno Luong am 21 Aug. 2020
alpha=0.01; lambda=0.99;
f=@(j) ((1-alpha).^j-(-alpha).^j).*lambda.^j*exp(lambda*alpha)./(factorial(j)*(exp(lambda)-1));
p=f(1:22); % f is practically 0 beyond 10
c=cumsum(p); c=c/c(end);
n = 100; % 1e6;
[~,j] = histc(rand(1,n),[0 c]);


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