Hypoexponential Distribution with Different Parameters

Abstract

The Hypoexponential distribution is the distribution of the sum of n ≥ 2 independent Exponential random variables. This distribution is used in moduling multiple exponential stages in series. This distribution can be used in many domains of application. In this paper we consider the case of n exponential Random Variable having distinct parameters. Using convolution, some properties of Laplace transform and the moment generating function, we analyse this case and give new properties and identities. Moreover, we shall study particular cases when i  are arithmetic and geometric.

Numerical Methods for Reliability and Safety Assessment

“…A given form of PDF and CDF can be found in Akkouchi (2008), Amari and Misra (1997), and Kordecki (1997). We give in this section a modified form of the PDF, CDF, reliability function, hazard function, MGF, and moment of order k of the particular case, see Smaili et al (2013b). Also, in the domain of reliability and performance evaluation of systems and software many authors used the geometric and arithmetic parameters such as (Gaudoin and Ledoux 2007;Jelinski and Moranda 1972;Moranda 1979).…”

“…However, the case when the parameters are identical the hypoexponential distribution is the Erlang distribution (Anjum and Perros 2011). Also the case when the parameters are distinct, it is known to be the hypoexponential distribution with different parameters discussed by Smaili et al (2013b).…”

The uniform continuity of characteristic function from convoluted exponential distribution with stabilizer constant

“…In other hand [2] has introduced properties of the characteristic function from geometric distribution as discrete version of the exponential distribution. Furthermore, the mathematical method to obtain the convolution of exponential distribution and its variations have been introduced in some works of [6], [7], [8].…”

Some properties of hypoexponential distribution with stabilizer constant

“…Akkouchi [5] used analytical method in convolution to find hypoexponential distribution. However, Smaili et al [4] used Laplace transform to find hypoexponential distribution. The hypoexponential distribution has many applications such as in communication system, computer science, queuing theory and markov processes.…”