Bivariate Gompertz generator of distributions: statistical properties and estimation with application to model football data

Abstract

In this paper, the bivariate extension of the so called Gompertz-G family was introduced and studied in detail. Marshall and Olkin shock model was used to build the proposed bivariate family. The new family was constructed from three independent Gompertz-H families using a minimisation process. Some of its statistical properties such as joint probability density function, coeffi cient of median correlation, moments, product moment, covariance, conditional probability density function, joint reliability function, stress-strength reliability and joint reversed (hazard) rate function were derived. After introducing the general class, three special models of the new family were discussed. Maximum likelihood method was used to estimate the family parameters. A simulation study was carried out to examine the bias and mean square error of the maximum likelihood estimators. Finally, the importance of the proposed bivariate family was illustrated by means of real dataset, and it was found that the proposed model provides better fi t than other well-known models in the statistical literature such as bivariate Gompertz, bivariate generalized Gompertz, bivariate Gumbel Gompertz, bivariate Burr X Gompertz and bivariate exponentiated Weibull-Gomperz

Investigating the Relationship between Processor and Memory Reliability in Data Science: A Bivariate Model Approach

“…Let X and Y be two random variables following the MExE distribution, then the marginal density functions are given by (11) respectively. For the conditional pdf of X given Y, it can be written as…”

“…In [8], the authors studied some families of bivariate Kumaraswamy distribution using different copulas. Others used the Marshall-Olkin bivariate copulas; one may refer to ( [9][10][11][12][13][14][15][16][17][18]). More recent work on bivariate models with copula functions with applications can be found in [19,20], among others.…”

Bivariate Discrete Odd Generalized Exponential Generator of Distributions for Count Data: Copula Technique, Mathematical Theory, and Applications

“…More detail is given in Balakrishnan and Lai [9]. The construction of the BV discrete and continuous distributions are mainly via (I) the copulas (II) compounding (III) marginals (IV) reduction and (V) conditioning, for instance, Johnson and Tenenbein [10], Quesada and Rodrguez [11], Fang et al [12], Durante [13], Kundu and Gupta [14], Sarabia et al [15], Roozegar and Jafari [16], Eliwa et al [17], among others.…”

Bivariate odd Weibull-G family of distributions: properties, Bayesian and non-Bayesian estimation with bootstrap confidence intervals and application

“…Recently, the trend in proposing new bivariate compounded (power series family), weighted and generalized (G-) families of distributions which have received increased attention. See for example, Sunoj and Nair [22], Nair and Sunoj [23], Kundu and Gupta [24], Domma [25], Sarhan et al [26], Kundu and Gupta [27], Barreto-Souza and Lemonte [28], Sarabia et al [29], Balakrishna and Shiji [30], El-Bassiouny et al [31], El-Gohary et al [32], Roozegar and Jafari [33], Ghosh and Hamedani [34], Ibrahim et al [35], Eliwa and El-Morshedy [36], Eliwa et al [37], El-Morshedy et al [38,39] and others.…”