Exact distribution of the convolution of negative binomial random variables

Xu Chen and Chang Guisong

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 6, 2851-2856

Abstract: In this note, we derive the exact distribution of S by using the method of generating function and BELL polynomials, where S = X1 + X2 + ⋅⋅⋅ + Xn, and each Xi follows the negative binomial distribution with arbitrary parameters. As a particular case, we also obtain the exact distribution of the convolution of geometric random variables.

Date: 2017
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DOI: 10.1080/03610926.2015.1053931

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