Comparative study of estimation methods for the Teissier distribution: performance evaluation and real-world applications

Teissier distribution is a flexible statistical model originally developed to describe biological mortality and aging processes, characterized by an increasing hazard rate that makes it suitable for time-to-event data. This study provides a comprehensive comparative analysis of 11 estimation methods for the Teissier distribution to establish guidelines for selecting the most effective method. The methods considered include maximum likelihood, moments, least squares, weighted least squares, percentile, maximum product of spacings, minimum spacing absolute distance, minimum spacing absolute-log distance, Cramér–von Mises, Anderson–Darling, and right-tail Anderson–Darling. Their performance is evaluated through extensive simulation studies using absolute bias, mean squared error, and empirical distribution function–based metrics. The estimators are further assessed using two real datasets to demonstrate their applicability across different empirical settings. The results show that maximum likelihood estimation is the most robust method, with maximum product of spacings and percentile estimation serving as effective alternatives.