Parametric Estimation for a new Pareto-type model Based on Constant-Stress Partially Accelerated Censoring data (European Journal of Pure and Applied Mathematics, 2025)
Verifying an item's lifespan under normal usage conditions requires more time and cost than it does under accelerated conditions if the item has a high level of reliability. To reduce the costs associated with testing the products without sacrificing quality, the items are subjected to higher stress levels than usual, resulting in early failures within a short period, which are called Accelerated Life Tests (ALTs). The primary focus of this study is to rigorously investigate precise estimation issues related to point and interval estimations for a New Pareto-Type (NPT) distribution under constant stress partially (ALTs) with type-I Generalized Hybrid Censored Samples (GHCS). In addition to using the Maximum Likelihood Estimates (MLEs), the Expectation–Maximization (EM) algorithm is utilized to obtain the point and interval estimates of the model parameters as well as the acceleration factor. The observed Fisher information matrix is computed. We propose Bayes estimates concerning various loss functions. For this purpose, we adopt Metropolis–Hastings (M–H) algorithm method. Asymptotic and bootstrap confidence intervals are derived. Asymptotic intervals are obtained using normal approximation to MLEs. The bootstrap intervals are computed using boot-t algorithm. Further, Highest Posterior Density  (HPD) credible intervals are constructed. Various estimates obtained in the theory are compared with the help of a Monte Carlo simulation study. Finally, a real data set is studied to show the applicability of the considered model.
Keywords: A new Pareto-type distribution; Accelerated life tests model; Type-I generalized hybrid censoring scheme; EM algorithm; Maximum likelihood estimation