Estimation of Past Vitality and Past Geometric Vitality Function in Weighted Power Model

Accepted July 2026

Abstract

In this study, we present a new framework for estimating the Past Vitality Function (PVF) and Past Geometric Vitality Function (PGVF) using the Weighted Power Distribution (WPD). We provide Maximum Likelihood Estimators (MLE) and Uniformly Minimum Variance Unbiased Estimators (UMVUE) for these measures, and describe their sampling distributions and asymptotic properties.
We test these estimators with simulations, showing they are more precise in bounded support settings than traditional unbounded models. We also apply our method to survival data, where the WPD gives a better fit and is simpler than other distributions. Our results offer improved tools for modeling reliability in systems with limited lifetimes.