Extension of the Bradford Distribution via Generalized Transmutation: Properties, Estimation and Application

Accepted July 2026

Abstract

This article proposes a novel family of probability distributions constructed using the T–X transformation approach, with the Bradford distribution serving as the baseline distribution. A wide range of fundamental mathematical characteristics is derived. The maximum likelihood approach is used to estimate the unknown parameters of the proposed model. Additionally, a Monte Carlo simulation analysis is conducted to evaluate the finite-sample performance of the suggested estimators. The analysis of the real-data application demonstrates that the proposed distribution provides the optimal fit compared to the other considered unit distributions.