Regarding the PDF and CDF of two gamma distributed random varaibles!!

3 次查看（过去 30 天）
kader
kader 2016-1-14
评论： Torsten 2016-1-18
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

请先登录，再回答此问题。

采纳的回答

Torsten
Torsten 2016-1-14
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 个评论
显示 8更早的评论
kader
kader 2016-1-16
But for me X1=gamma(a,m) and X2=gamma(a,m), then what will be the pdf and cdf of
Torsten
Torsten 2016-1-18
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.

请先登录，再进行评论。

更多回答（1 个）

the cyclist
the cyclist 2016-1-14
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).

类别

在 Help Center 和 File Exchange 中查找有关 Descriptive Statistics 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by