A New Probability-Based Parametric Model for Modeling Time-to-Event Datasets

This paper introduces a new probability-based parametric model, called the weighted harmonic inverted exponential (WHIE) distribution, to model positive continuous data. The proposed model is developed using the weighted harmonic mean transformation and is motivated by extensions of survival-based distributions. Some key statistical properties of the WHIE distribution are derived, and mathematical expressions for different methods of parameter estimation are presented. A Monte Carlo simulation study is conducted to assess the performance of these estimation methods in terms of accuracy and precision. To demonstrate its practical applicability, the proposed distribution is fitted to two hydrological datasets. The results show that the WHIE distribution provides a flexible and competitive fit compared to existing models. The findings suggest that the WHIE distribution is a useful alternative for modeling positive continuous data that exhibit diverse structural characteristics.