This study presents a new three-parameter beta distribution defined on the unit interval, which can have increasing, decreasing, left-skewed, right-skewed, approximately symmetric, bathtub, and upside-down bathtub shaped densities, and increasing, U, and bathtub shaped hazard rates. This model can define well-known distributions with various parameters and supports, such as Kumaraswamy, beta exponential, exponential, exponentiated exponential, uniform, the generalized beta of the first kind, and beta power distributions. We present a comprehensive account of the mathematical features of the new model. Maximum likelihood methods and a Bayesian method under squared error and linear exponential loss functions are presented; also, approximate confidence intervals are obtained. We present a simulation study to compare all the results. Two real-world data sets are analyzed to demonstrate the utility and adaptability of the proposed model.

In this paper, relations between moments of dual generalized order statistics from a exponentiated generalized class of distributions, given by Cardeiro et al. (2013) are studied. Some particular cases of dual generalized order statistics and examples based on it are discussed. The characterization of given distribution based on moment properties is also presented.

The Bayesian prediction of future failures from Lomax distribution is the subject of this research. The observed data is censored using a Type‐I hybrid censoring scheme under a step‐stress partially accelerated life test. There are two types of sampling schemes considered: one‐sample and two‐sample. We create predictive intervals for failure observations in the future. Bayesian prediction intervals are constructed using MCMC algorithms. After all, two numerical examples, simulation study and a real‐life example are provided for both one‐sample and two‐sample methods for the purpose of illustration.

In this paper, the problem of Bayesian prediction intervals for a future observations from weighted exponential distribution is concerned. Constant-stress partially accelerated life test under Type-II hybrid censoring scheme of the observed data is used. One- and two-sample Bayesian prediction intervals for a future observations based on Type-II hybrid censored data are derived. Markov Chain Monte Carlo (MCMC) technique is used to find Bayesian predictive intervals because one- and two-sample Bayesian predictive survival function cannot be obtained in closed-form. Finally, some numerical results are presented to illustrate all the inferential results developed in this paper.

The generalized order statistics is a unified model of several ordered random schemes such as order statistics, record values, progressive type II right censored order statistics, etc. Order statistics and record values appear in many statistical applications and are widely used in statistical modeling and inference. Progressive Type-II censored sampling scheme is a versatile censoring scheme because it allows the experimenter to save time and cost of the life-testing experiment and is quite useful in reliability and lifetime studies. Rayleigh distribution and its extended version such as modified weighted Rayleigh distribution are important distributions for modeling lifetime data in reliability analysis and engineering science. In this paper, we studied moment properties of generalized order statistics from modified weighted Rayleigh distribution. Further, characterization results based on moment properties and conditional expectation are presented. The simulation studies based on order statistics, upper record values, and progressive type II right censored order statistics are also carried out.