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

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

The primary objective of this article was to introduce a new probabilistic model for the discussion 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 both Y=max{X1,X2} and W=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.

A New Flexible Univariate and Bivariate Family of Distributions for Unit Interval (0, 1)

We propose a new generator for unit interval which is used to establish univariate and bivariate families of distributions. The univariate family can serve as an alternate to the Kumaraswamy-G univariate family proposed earlier by Cordeiro and de-Castro in 2011. Further, the new generator can also be used to develop more alternate univariate and bivariate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G and Transmuted-G for support (0, 1). Some structural properties of the univariate family are derived and the estimation of parameters is dealt. The properties of a special model of this new univariate family called a New Kumaraswamy-Weibull (NKwW) distribution are obtained and parameter estimation is considered. A Monte Carlo simulation is reported to assess NKwW model parameters. The bivariate extension of the family is proposed and the estimation of parameters is described. The simulation study is also conducted for bivariate model. Finally, the usefulness of the univariate NKwW model is illustrated empirically by means of three real-life data sets on Air Conditioned Failures, Flood and Breaking Strength of Fibers, and one real-life data on UEFA Champion’s League for bivariate model.

Discrete Gompertz-G Family of Distributions for Over- and Under-Dispersed Data with Properties, Estimation, and Applications

Alizadeh et al. introduced a flexible family of distributions, in the so-called Gompertz-G family. In this article, a discrete analogue of the Gompertz-G family is proposed. We also study some of its distributional properties and reliability characteristics. After introducing the general class, three special models of the new family are discussed in detail. The maximum likelihood method is used for estimating the family parameters. A simulation study is carried out to assess the performance of the family parameters. Finally, the flexibility of the new family is illustrated by means of four genuine datasets, and it is found that the proposed model provides a better fit than the competitive distributions.

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

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.