We obtain explicit expressions for single and product moments of the order statistics of an omega distribution. We also discuss seven methods to estimate the omega parameters. Various simulation results are performed to compare the performance of the proposed estimators. Furthermore, the maximum likelihood method is adopted to estimate the omega parameters under the type II censoring scheme. The usefulness of the omega distribution is proven using a real data set.

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.