A Bivariate Extension to Exponentiated Inverse Flexible Weibull Distribution: Shock Model, Features, and Inference to Model Asymmetric Data, By Morad Alizadeh

Research

Title	A Bivariate Extension to Exponentiated Inverse Flexible Weibull Distribution: Shock Model, Features, and Inference to Model Asymmetric Data
Type	Article
Keywords	statistical model; Marshall–Olkin shock model; marginal distributions; simulation; comparative study; statistics and numerical data
Journal	SYMMETRY-BASEL
DOI	—
Researchers	Mahmoud El-Morshedy (First researcher) , Mohammed Eliwa (Second researcher) , Muhammad Tahir (Third researcher) , Morad Alizadeh (Fourth researcher) , Rana El-Desokey (Fifth researcher) , Afrah Al-Bossly (Not in first six researchers) , Hana Alqifari (Not in first six researchers)

Abstract

The primary objective of this article was to introduce a new probabilistic model for the dis- cussion and analysis of random covariates. The introduced model was derived based on the Marshall– Olkin shock model. After proposing the mathematical form of the new bivariate model, some of its distributional properties, including joint probability distribution, joint reliability distribution, joint reversed (hazard) rate distribution, marginal probability density function, conditional probability density function, moments, and distributions for bothY = max{X1,X2} andW = min{X1,X2}, were investigated. This novel model can be applied to discuss and evaluate symmetric and asymmetric data under various kinds of dispersion. Moreover, it can be used as a probability approach to analyze different shapes of hazard rates. The maximum likelihood approach was utilized for estimating the parameters of the bivariate model. A simulation study was carried out to assess the performance of the parameters, and it was noted that the maximum likelihood technique can be used to generate consistent estimators. Finally, two real datasets were analyzed to illustrate the notability of the novel bivariate distribution, and it was found that the suggested distribution provided a better fit than the competitive bivariate models.