Bivariate Burr X Generator of Distributions: Properties and Estimation Methods with Applications to Complete and Type-II Censored Samples

Abstract

Burr proposed twelve different forms of cumulative distribution functions for modeling data. Among those twelve distribution functions is the Burr X distribution. In statistical literature, a flexible family called the Burr X-G (BX-G) family is introduced. In this paper, we propose a bivariate extension of the BX-G family, in the so-called bivariate Burr X-G (BBX-G) family of distributions based on the Marshall-Olkin shock model. Important statistical properties of the BBX-G family are obtained, and a special sub-model of this bivariate family is presented. The maximum likelihood and Bayesian methods are used for estimating the bivariate family parameters based on complete and Type II censored data. A simulation study was carried out to assess the performance of the family parameters. Finally, two real data sets are analyzed to illustrate the importance and the flexibility of the proposed bivariate distribution, and it is found that the proposed model provides better fit than the competitive bivariate distributions.

Marshall Olkin Alpha Power Extended Weibull Distribution: Different Methods of Estimation based on Type I and Type II Censoring

“…We suggest studying a more flexible censored sample for the proposed distribution in future studies, such as [38,39]. We suggest researching multivariate analysis, such as [40,41] for the proposed distribution.…”

A New Kumaraswamy Generalized Family of Distributions with Properties, Applications and Bivariate Extension

“…In this Section, we introduce a bivariate extended of the NKw-G family according to Marshall and Olkin shock model (see, Marshall and Olkin, [43]). Several authors used the Marshall and Olkin approach as a method to generate bivariate distributions, see Sarhan and Balakrishnan, [44], Kundu and Dey [45], El-Gohary et al [46], Muhammed [47], El-Bassiouny et al [48], Ghosh and Hamedani [49], El-Morshedy et al [50,51], Eliwa et al [52], Hussain et al [53], and others. The BvNKw-G family is constructed from three independent NKw-G families by utilizing a minimization process.…”

Marshall–Olkin Alpha Power Weibull Distribution: Different Methods of Estimation Based on Type‐I and Type‐II Censoring

“…e handled data from all such mentioned trials are called censored data. Censored test has many types and the most important and used schemes are Type-I censored and Type-II censored; see, for example, the works of Balakrishnan and Ng [18], El-Morshedy et al [19], and Almetwally et al [20]. is paper's aim is to introduce a new lifetime distribution defined as Marshall-Olkin alpha power Weibull (MOAPW) distribution, depending on the MOAP family.…”