Modeling, Estimation, and Novel Prediction Approach via Maximum Product Spacing for Unit Linear Hazard Rate Distribution Under Type-II Censoring

This paper presents the first comprehensive inferential framework for the unit linear hazard rate distribution under Type-II censoring. The unit linear hazard rate distribution is a flexible two-parameter bounded lifetime model obtained by transforming the classical linear hazard rate distribution. It accommodates a wide range of density and hazard rate shapes, including increasing and bathtub forms, making it suitable for modeling proportions, normalized lifetimes, and bounded reliability data. Its fundamental statistical properties are established through analytical, numerical, and graphical investigations. Parameter estimation under Type-II censoring is developed using maximum likelihood and maximum product spacing methods. Although maximum likelihood estimation enjoys standard asymptotic properties, the maximum product spacing approach offers superior numerical stability and competitive finite-sample performance, particularly under heavy censoring. Bootstrap confidence intervals based on the maximum product spacing estimators are also constructed. In addition, novel point and interval prediction procedures for future censored observations are developed using conditional distributions, predictive likelihood, and a maximum product spacing-based predictive framework. Extensive Monte Carlo simulations demonstrate the effectiveness of the proposed methods, while two real data applications illustrate the flexibility and superior practical performance of the proposed model compared with several competing lifetime distributions.