A Generalization of the Exponential-Logarithmic Distribution

Generalizing distributions is an old practice and has ever been considered as precious as many other practical problems in statistics. It simply started with defining different mathematical functional forms, and then induction of location, scale or inequality parameters. The generalization through induction of shape parameter(s) started in 1997, and the last two decades were full of such practices. But to cope with the complex situations under series and parallel structures, the art of mixing discrete and continuous started in 1998. In this article, we present a survey on compounding univariate distributions, their extensions and classes. We review several available compound classes and propose some new ones. The recent trends in the construction of generalized and compounding classes are discussed, and the need for future works are addressed.

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“…Pappas et al (2015) applied the LA1 class to the ELn cdf given in Eq. (8), and obtained the cdf of the generalized ELn (GELn) distribution as…”

Section: Exponential-logarithmic (Eln)mentioning

confidence: 99%

Compounding of distributions: a survey and new generalized classes

2016

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“…Similarly, Adamidis and Loukas (1998) introduced exponential geometric distribution, while Silva et al (2010) come up with the generalized exponential geometric distribution. Tahmasbi and Rezaei (2008) introduced exponential-logarithmic distribution similarly, Pappas et al (2015) proposed a generalized exponential-logarithmic. Silva and Cordeiro (2015) introduced a new class of distribution called the BurrXII Poisson distribution and recently Muhammad (2016a) proposed generalized BurrXII Poisson distribution.…”

Section: Introductionmentioning

confidence: 99%

Generalized half-logistic Poisson distributions

Muhammad

2017

CSAM

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In this article, we proposed a new three-parameter distribution called generalized half-logistic Poisson distribution with a failure rate function that can be increasing, decreasing or upside-down bathtub-shaped depending on its parameters. The new model extends the half-logistic Poisson distribution and has exponentiated half-logistic as its limiting distribution. A comprehensive mathematical and statistical treatment of the new distribution is provided. We provide an explicit expression for the r th moment, moment generating function, Shannon entropy and Rényi entropy. The model parameter estimation was conducted via a maximum likelihood method; in addition, the existence and uniqueness of maximum likelihood estimations are analyzed under potential conditions. Finally, an application of the new distribution to a real dataset shows the flexibility and potentiality of the proposed distribution.

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Information approach for a lifetime change-point model based on the exponential-logarithmic distribution

Chen

Ning

2018

Communications in Statistics - Simulation and Computation

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A Generalization of the Exponential-Logarithmic Distribution

Cited by 3 publications

References 6 publications

Compounding of distributions: a survey and new generalized classes

Compounding of distributions: a survey and new generalized classes

Generalized half-logistic Poisson distributions

Information approach for a lifetime change-point model based on the exponential-logarithmic distribution

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