Regarding the PDF and CDF of two gamma distributed random varaibles!!
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If X ~ gamma (m, p) with a shape parameter m and a scale parameter p and Y~ gamma (m, q) with a shape parameter m and a scale parameter q when X and Y are independent random variables then What will be the PDF and CDF of X+Y? How can I solve it in MatLab
Thanks in advance for help
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Accepted Answer
Torsten
on 14 Jan 2016
The density function for X+Y is given by
f_X+Y(z)=exp(-q*z)*p^(2*m)/(gamma(m))^2*integral_{x=0}^{x=z}(x*(z-x))^(m-1)*exp(-(p-q)*x) dx
Use MATLAB's "integral" to evaluate the integral for different values of z.
Best wishes
Torsten.
10 Comments
Torsten
on 18 Jan 2016
X0+X1 ~ gamma(2*a,m)
In general:
X0+X1+...+Xn ~ Gamma((n+1)*a,m)
To calculate pdf and cdf, use gampdf and gamcdf.
Best wishes
Torsten.
More Answers (1)
the cyclist
on 14 Jan 2016
This is a math or stats question, not a MATLAB question. But, you made me curious.
The answer is not trivial. This paper gives a solution. This post on another forum gives an explanation (and references the paper I just mentioned).
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