Probability-Moments and Cumulants (ISS Statistics Paper I (Old Subjective Pattern)): Questions 1 - 1 of 1
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Question number: 1
» Probability » Moments and Cumulants
Appeared in Year: 2013
Essay Question▾
Describe in Detail
Compute the factorial moments µ (r) and the cumulants k r, r = 1, 2, …. . , of Poisson distribution with parameter m.
Explanation
Let X follows Poisson distribution with parameter m. The density function is
The r th factorial moment of Poisson distribution is
The cumulants of Poisson distribution is
we known that the moment generating function of X is
So, the cumulants is… (26 more words) …