The Real Powers of the Convolution of a Gamma Distribution and a Bernoulli Distribution

Ben Salah Nahla () and Masmoudi Afif ()
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Ben Salah Nahla: Sfax University
Masmoudi Afif: Sfax University

Journal of Theoretical Probability, 2011, vol. 24, issue 2, 450-453

Abstract: Abstract In this paper, we essentially compute the set of x,y>0 such that the mapping $z\longmapsto(1-r+re^{z})^{x}(\frac{\lambda}{\lambda-z})^{y}$ is a Laplace transform. If X and Y are two independent random variables which have respectively Bernoulli and Gamma distributions, we denote by μ the distribution of X+Y. The above problem is equivalent to finding the set of x>0 such that μ *x exists.

Keywords: Bernoulli law; Convolution power; Gamma distribution; Jørgensen set; Laplace transform; 60E10; 33A65 (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10959-009-0253-3

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