A generalization of the exponential-Poisson distribution

By W. Barreto‐Souza, Francisco Cribari‐Neto. 2008

154 citations recorded by the source corpus.

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 Renyi and Shannon entropies are given and an application using a real data set is presented. Finally, simulation results on maximum likelihood estimation are presented.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/77a62f4a63ec85c9dea616ed822c799a8a5c04e1

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

A new two parameter lifetime distribution: model and properties (2012, methodology): “A three-parameter extension of the EP distribution was obtained by Barreto-Souza and Cribari-Neto [5].”
A new compounding life distribution: the Weibull–Poisson distribution (2012, methodology): “In Example 2, we use the parameter estimation procedure of Wagner and Francisco [3] for the EP model.”
The complementary exponential power series distribution (2013, methodology): “The distribution proposed by Kus (2007) was generalized by including a power parameter in his distribution, by Barreto-Souza and Cribari-Neto (2009).”
A new lifetime model with decreasing failure rate (2010, methodology): “[8] W. Barreto-Souza and F. Cribari-Neto, A generalization of the exponential–Poisson distribution, Statist.”
The complementary Weibull geometric distribution (2014, background): “Barreto-Souza and Cribari-Neto [4], generalizes the distribution proposed by Kus [10], including a new parameter in its distribution, which makes its risk function more flexible.”
A new lifetime distribution (2014, methodology): “This distribution known as the generalized exponential Poisson (GEP) has decreasing, increasing and upside-down bathtub hazard rates.”