In this paper, a bivariate Burr Type III distribution is constructed and some of its statistical properties such as bivariate probability density function and its marginal, joint cumulative distribution and its marginal, reliability and hazard rate functions are studied. The joint probability density function and the joint cumulative distribution are given in closed forms. The joint expectation of this distribution is proposed. The maximum likelihood estimation and prediction for a future observation are derived. Also, Bayesian estimation and prediction are considered under squared error loss function. The performance of the proposed bivariate distribution is examined using a simulation study. Finally, a data set is analyzed under the proposed distribution to illustrate its flexibility for real-life application.

Accelerated life testing or partially accelerated life tests is very important in life testing experiments because it saves time and cost. Partially accelerated life tests are used when the data obtained from accelerated life tests cannot be extrapolated to usual conditions. This paper proposes, constant–stress partially accelerated life test using Type II censored samples, assuming that the lifetime of items under usual condition have the Topp Leone-inverted Kumaraswamy distribution. The Bayes estimators for the parameters, acceleration factor, reliability and hazard rate function are obtained. Bayes estimators based on informative priors is derived under the balanced square error loss function as a symmetric loss function and balanced linear exponential loss function as an asymmetric loss function. Also, Bayesian prediction (point and bounds) is considered for a future observation based on Type-II censored under two samples prediction. Numerical studies are given and some interesting comparisons are presented to illustrate the theoretical results. Moreover, the results are applied to real data sets.

In this paper, bivariate compound exponentiated survival function of the Lomax distribution is constructed based on the technique considered by AL-Hussaini (2011). Some properties of the distribution are derived. Maximum likelihood estimation and prediction of the future observations are considered. Also, Bayesian estimation and prediction are studied under squared error loss function. The performance of the proposed bivariate distribution is examined using a simulation study. Finally, a real data set is analyzed under the proposed distribution to illustrate its flexibility for real-life application.

In this paper constant stress accelerated life tests are discussed based on Type II censored sampling from Marshall-Olkin extended Burr Type X Distribution. The model parameters and the acceleration factor are estimated using the maximum likelihood estimation method and two-sample predictions are considered for future order statistics. Further, the asymptotic confidence intervals for the model parameters are discussed. Numerical study is given, and some interesting comparisons are presented to illustrate the theoretical results. Moreover, the results are applied on real dataset.

Burr Type III distribution have been mainly used in statistical modeling of events in a variety of applied mathematical contexts such as fracture roughness, life testing, meteorology, modeling crop prices, forestry, reliability analysis. Our aim of this work is to construct a bivariate Burr Type III distribution and some of its structural properties such as bivariate probability density function and it ' s marginal, joint cumulative distribution and it ' s marginal, reliability and hazard rate function are studied. The maximum likelihood estimators of the parameters are derived. The Bayes estimators of the parameters based on the squared error loss function and Bayesian prediction of the future observations are presented. The performance of the proposed bivariate distribution is examined using a simulation study. Finally, one data set under the proposed distributions to illustrate their flexibility for real-life applications is analyzed.