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.
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.
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