A generalization of the exponential-Poisson distribution

Abstract

The two-parameter distribution known as exponential-Poisson (EP) distribution, which has decreasing failure rate, was introduced by Kus (2007). In this paper we generalize the EP distribution and show that the failure rate of the new distribution can be decreasing or increasing. The failure rate can also be upside-down bathtub shaped. A comprehensive mathematical treatment of the new distribution is provided. We provide closed-form expressions for the density, cumulative distribution, survival and failure rate functions; we also obtain the density of the ith order statistic. We derive the rth raw moment of the new distribution and also the moments of order statistics. Moreover, we discuss estimation by maximum likelihood and obtain an expression for Fisher's information matrix. Furthermore, expressions for the Rényi and Shannon entropies are given and estimation of the stress-strength parameter is discussed. Applications using two real data sets are presented.

A Resilience Parameter Model Generated by a Compound Distribution

“…It seems that mgf of an EGEG(p, β, α, γ) distribution is not easily found directly from the density function given in (9). Hence, we first obtain an alternative expression for the density function of the EGEG(p, β, α, γ) distribution using the series representation…”

“…Nadarajah and Kotz [8] presented four exponentiated type distributions that extend the standard gamma, standard Weibull, standard Gumbel, and standard Fréchet distributions. In addition, as some recent works, we can address the generalized exponentialPoisson (GEP) distribution proposed by Barreto-Souza and Cribari-Neto [9], the generalized modified Weibull (GMW) distribution proposed by Carrasco et al [10], and the generalized exponential geometric (GEG) distribution given by Silva et al [1] which extend the exponential-Poisson distribution of Kus [11], the modified Weibull distribution of Lai et al [12], and the exponential-geometric (EG) distribution of Adamidis and Loukas [13], respectively. An alternative version of the GEG distribution is also given in [14].…”

Estimation of the Parameters of Poisson-Exponential Distribution Based on Progressively Type II Censoring Using the Expectation Maximization (Em) Algorithm

“…Since the distribution is obtained through the compounding of poisson and exponential. Further Barreto and Cribari [2] generalized the distribution proposed by Kus by including a power parameter. Cancho et al [3] proposed a new family of distribution, called Poisson-Exponential (PE) distribution having increasing failure rate.…”

Algorithms of Confidence Intervals of WG Distribution Based on Progressive Type-II Censoring Samples

“…The Weibull-geometric (WG), Exponential-Poisson (EP), Weibull-Power-Series (WPS), Complementary-Exponential-geometric (CEG), Exponential-Geometric (EG), Generalized-Exponential-Power-Series (GEPS), Exponential Weibull-Poisson (EWP), and Generalized-Inverse-Weibull-Poisson (GIWP) distributions are introduced and presented by Adamidis and Loukas [5], Kus [6], Chahkandi and Ganjali [7], Tahmasbi and Rezaei [8], Barreto [9], Morais and Barreto [10], Barreto and Cribari [11], Louzada et al [12], and Cancho et al [13]. Hamedani and Ahsanullah [14] studied and discussed many properties of WG, such as moments, hazard functions, and functions of order statistics.…”