Constructions of Discrete Bivariate Distributions

Lai, C. D.

doi:10.1007/0-8176-4487-3_3

Cited by 20 publications

(14 citation statements)

References 50 publications

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“…There were three survey papers: Lai (2004;2006) and Sarabia and Gómez-Déniz (2008). The latest monograph by Balakrishnan and Lai (2009) provided an excellent overview.…”

Section: Journal Of Statistical Planning and Inference (November 2009)mentioning

confidence: 99%

Recent developments on the construction of bivariate distributions with fixed marginals

Lin

Dou

Kuriki

et al. 2014

J Stat Distrib Appl

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Constructing a bivariate distribution with specific marginals and correlation has been a challenging problem since 1930s. In this survey we shall focus on the recent developments on the FGM-related distributions, including Sarmanov and Lee's distributions, Baker's distributions and Bayramoglu's distributions. This complements the most recent works of (i) the review by Sarabia and Gómez-Déniz (2008, SORT) and (ii) the monograph by Balakrishnan and Lai (2009, Springer). Some new results are provided. Mathematics Subject Classification (2000): 62H20; 62H86; 62G30; 60E05; 62E10

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“…There were three survey papers: Lai (2004;2006) and Sarabia and Gómez-Déniz (2008). The latest monograph by Balakrishnan and Lai (2009) provided an excellent overview.…”

Section: Journal Of Statistical Planning and Inference (November 2009)mentioning

confidence: 99%

Recent developments on the construction of bivariate distributions with fixed marginals

Lin

Dou

Kuriki

et al. 2014

J Stat Distrib Appl

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“…A detailed review on construction of multivariate distributions using different approaches can be found in [23]. Methods of constructing bivariate distributions under discrete and continuous set up are available in [16] and [17] respectively. One simple method of constructing bivariate family of distributions using marginals was proposed by Morgenstern [20].…”

Section: Introductionmentioning

confidence: 99%

Morgenstern type bivariate Lindley Distribution

Vaidyanathan

Varghese

2016

Stat., optim. inf. comput.

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In this paper, a bivariate Lindley distribution using Morgenstern approach is proposed which can be used for modeling bivariate life time data. Some characteristics of the distribution like moment generating function, joint moments, Pearson correlation coefficient, survival function, hazard rate function, mean residual life function, vitality function and stress-strength parameter R = P r(Y < X), are derived. The conditions under which the proposed distribution is an increasing (decreasing) failure rate distribution and positive (negative) quadrant dependent is discussed. Also, the method of estimating model parameters and stress-strength parameter by maximum likelihood is elucidated. Numerical illustration using simulated data is carried out to access the estimates in terms of mean squared error and relative absolute bias.Keywords Farlie-Gumbel-Morgenstern family, maximum likelihood estimation, mean residual life, mean squared error, positive quadrant dependence, relative absolute bias, stress-strength parameter, vector hazard rate, vitality function AMS 2010 subject classifications 60E05

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“…Among the methods to generate bivariate distributions that are associated with bivariate EEGD are the compounding, trivariate reduction, copula approach and Sarmanov approach. For a survey on this topic, one may refer to Lai ().…”

Section: Methods For Generating Bivariate Discrete Distributionsmentioning

confidence: 99%

Review of univariate and bivariate exponentiated exponential‐geometric distributions

Famoye

Lee

2019

WIREs Computational Stats

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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

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Constructions of Discrete Bivariate Distributions

Cited by 20 publications

References 50 publications

Recent developments on the construction of bivariate distributions with fixed marginals

Recent developments on the construction of bivariate distributions with fixed marginals

Morgenstern type bivariate Lindley Distribution

Review of univariate and bivariate exponentiated exponential‐geometric distributions

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