Poisson Process for 500 variates
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Zeynep Toprak
on 13 May 2020
Commented: Najme Benvari
on 25 May 2023
I would like to generate a code to produce a poisson process for N = 500 variates witk k is randomly between 1 and 10 and lambda = 12.
N = 500;
T = 1;
lambda = 12;
t = linspace(0, T, 100);
dt = t(2) - t(1);
S=cumsum([zeros(1,N); poissrnd(lambda*dt, length(t)-1, N) ]);
plot(t,S)
I generated this code by myself, bu I cannot use the random value of k between 1 and 10 , and 500-variates graph has too many lines, but I guess this result is totally wrong, how can I get rid of my mistakes and write the code properly?
Thanks a lot.
My second code is this
T = 1;
lambda = 12;
k=9;
t = linspace(0, T, 500);
for i = 1:500
f(i) = (lambda.^k) .* exp(-lambda) ./ factorial(k);
end
N = cumsum(f);
disp(N)
stairs(t,N(1:100))
But, again, the graph and estimations are totally wrong.
0 Comments
Accepted Answer
Abdullah Gül
on 31 May 2020
Hello Zeynep,
You may try this.
lambda = 12;
nPeriods = 500;
dt = 0.1; %time steps
T = nPeriods*dt;
t = 0:0.1:T;
rng('default')
k=randi([1,10],1,nPeriods);
f = (lambda.^k).*exp(-lambda)./factorial(k); % Poission Dist.
Nd = cumsum(f);
N = [ 0 Nd(1:end) ]; % N(0)=0.
stairs(t,N)
If you decrease the Nperiods, you could see the stairs more precisely.
3 Comments
Abdullah Gül
on 31 May 2020
The difference between them comes from randomness. I mean when you want to simulate a series of discrete events(e.g. Poisson dist.), its name becomes Poisson process. Here, the timing of events is random, but your model is still Poisson. Hence, you could use that code.
More Answers (3)
Sulaymon Eshkabilov
on 14 May 2020
Here is the alternative solution:
T = 1;
lambda = 12;
t = linspace(0, T, 500);
k=randi([1,10], 500);
f = (lambda.^k) .* exp(-lambda) ./ factorial(k);
N = sum(f);
disp(N);
stairs(t,N)
Good luck
Sulaymon Eshkabilov
on 14 May 2020
Why not to use MATLAB's built in fcn: poissrnd()
3 Comments
Sa'adatu Abubakar
on 29 Jul 2021
Hello I'm also interested in the area please can you help me with the MATLAB code for poison arrival and general servive with single server?. Thank you
Sa'adatu Abubakar
on 29 Jul 2021
please I mean poisson arrival with general service and single server.
Najme Benvari
on 23 May 2023
Hi I read the Poisson production code when the jump size is random and the intensity of the jumps is Stochastic and a CIR process. I will be very thankful.
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