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Review of univariate and bivariate exponentiated exponential‐geometric distributions
Author(s) -
Famoye Felix,
Lee Carl
Publication year - 2019
Publication title -
wiley interdisciplinary reviews: computational statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.693
H-Index - 38
eISSN - 1939-0068
pISSN - 1939-5108
DOI - 10.1002/wics.1481
Subject(s) - mathematics , natural exponential family , univariate , exponential family , bivariate analysis , exponential function , exponential distribution , univariate distribution , statistics , exponentially modified gaussian distribution , geometric distribution , gamma distribution , probability distribution , multivariate statistics , mathematical analysis
The exponentiated exponential (or generalized exponential) distribution is a two‐parameter right skewed unimodal density function. A discrete analogue of the distribution is often called the exponentiated exponential‐geometric (or discrete generalized exponential) distribution. We review some methods for generating discrete analogues of the exponentiated exponential distribution and discuss some of their properties. Among the important properties of the univariate distribution are (a) closed form cumulative distribution function and probability mass function and (b) ability to accommodate under‐, equi‐, or over‐dispersion. Some methods to extend the univariate distribution to the bivariate exponentiated exponential‐geometric distribution are discussed. The extension of univariate and bivariate distributions to count data regression models is briefly described. It is expected that this review will serve as a reference and encourage further research work and generalizations of the exponentiated exponential‐geometric distribution. This article is categorized under: Statistical Models > Linear Models Data: Types and Structure > Categorical Data Statistical Models > Generalized Linear Models