Therrar Kadri, Khaled Smaili
Department of Mathematics
Faculty of Sciences
Beirut Arab University
Beirut, LEBANON
Department of Applied Mathematics
Faculty of Sciences
Lebanese University
Zahle, LEBANON

Abstract. The sum of random variables are of interest in many areas of the sciences. In teletraffic analysis, the sum of Hyperexponential distribution is used as a model for the holding time distribution. Many authors examined this model and discussed its probability density function. In this paper, we consider the sum of independent Hyper-Erlang distributions. We showed that the probability density function of this distribution is related to probability density function of the sum of independent Erlang distributions- the Hypoexponential distribution. As a consequence, we find an exact closed expressions for the probability density function of both distribution, which are related to the Kummer confluent hypergeometric function.

Received: August 29, 2014

AMS Subject Classification: 62E15, 60E10, 60E05

Key Words and Phrases: convolution distribution, hyper-Erlang distribution, hypoexponential distribution, Erlang distribution, probability density, Bessel functions, confluent hypergeometric function

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