Generalized convolution product of an infinitely divisible distribution and a Bernoulli distribution

Ben Salah Nahla

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 20, 7297-7304

Abstract: In this paper, we essentially characterize the real power of the convolution set of X + Y, where X and Y≥0 are two independent random variables which have respectively a Bernoulli distribution, with parameter r∈(0,1), and an infinitely divisible probability distribution ν. The above problem is equivalent to finding the set of x,y≥0 such that the mapping z↦(1−r+rez)x(E(ezY))y is a Laplace transform of some probability distribution. This class of real power of convolution x is provided and described. The obtained results generalize the case where Y is Gamma or Negative Binomial distributed.

Date: 2022
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DOI: 10.1080/03610926.2021.1879863

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