Exponentiated exponential (EE) model has been used effectively in reliability, engineering, biomedical, social sciences, and other applications. In this study, we introduce a new bivariate mixture EE model with two parameters assuming two cases, independent and dependent random variables. We develop a bivariate mixture starting from two EE models assuming two cases, two independent and two dependent EE models. We study some useful statistical properties of this distribution, such as marginals and conditional distributions and product moments and conditional moments. In addition, we study a dependent case, a new mixture of the bivariate model based on EE distribution marginal with two parameters and with a bivariate Gaussian copula. Different methods of estimation for the model parameters are used both under the classical and under the Bayesian paradigm. Some simulation studies are presented to verify the performance of the estimation methods of the proposed model. To illustrate the flexibility of the proposed model, a real dataset is reanalyzed.
To study the heterogeneous nature of lifetimes of certain mechanical or engineering processes, a mixture model of some suitable lifetime distributions may be more appropriate and appealing as compared to simple models. This paper considers a mixture of the Marshall–Olkin extended Weibull distribution for efficient modeling of failure, survival, and COVID-19 data under classical and Bayesian perspectives based on type-II censored data. We derive several properties of the new distribution such as moments, incomplete moments, mean deviation, average lifetime, mean residual lifetime, Rényi entropy, Shannon entropy, and order statistics of the proposed distribution. Maximum likelihood and Bayes procedure are used to derive both point and interval estimates of the parameters involved in the model. Bayes estimators of the unknown parameters of the model are obtained under symmetric (squared error) and asymmetric (linear exponential (LINEX)) loss functions using gamma priors for both the shape and the scale parameters. Furthermore, approximate confidence intervals and Bayes credible intervals (CIs) are also obtained. Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimators and Bayes estimators with respect to their estimated risk. The flexibility and importance of the proposed distribution are illustrated by means of four real datasets.
A new family of distributions called the mixture of the exponentiated Kumaraswamy-G (henceforth, in short, ExpKum-G) class is developed. We consider Weibull distribution as the baseline (G) distribution to propose and study this special sub-model, which we call the exponentiated Kumaraswamy Weibull distribution. Several useful statistical properties of the proposed ExpKum-G distribution are derived. Under the classical paradigm, we consider the maximum likelihood estimation under progressive type II censoring to estimate the model parameters. Under the Bayesian paradigm, independent gamma priors are proposed to estimate the model parameters under progressive type II censored samples, assuming several loss functions. A simulation study is carried out to illustrate the efficiency of the proposed estimation strategies under both classical and Bayesian paradigms, based on progressively type II censoring models. For illustrative purposes, a real data set is considered that exhibits that the proposed model in the new class provides a better fit than other types of finite mixtures of exponentiated Kumaraswamy-type models.
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