Finding the PDF of the hypoexponential random variable using the Kad matrix similar to the general Vandermonde matrix

Khaled Smaili, Therrar Kadri and Seifedine Kadry

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 5, 1542-1549

Abstract: The sum of independent exponential random variables – the hypoexponential random variables – plays an important role of modeling in many domains. Khuong and Kong in (2006) were concerned in evaluating the performance of some diversity scheme, which deals with the problem of finding the probability density function of this hypoexponential random variable. They considered a particular case of m independent exponential random variable, when l random variables have the same mean and m − l remaining random variables of different means and they found a closed expression of its probability density function. In this paper, we consider the general case of the hypoexponential random variable when the means do not have to be distinct. We find a more simple and general closed expression of its probability density function than that of Khuong and Kong. This expression is obtained using a new defined matrix called the Kad matrix, which is similar to the general Vandermonde matrix. Eventually, we present an application illustrating our work.

Date: 2016
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DOI: 10.1080/03610926.2014.930910

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