On Generalized Transmuted Lifetime Distribution

TL;DR

This paper introduces a new generalized transmuted lifetime distribution encompassing many existing distributions, providing comprehensive mathematical properties, estimation methods, and real-data applications.

Contribution

The paper proposes a novel generalized transmuted lifetime distribution with extensive mathematical properties and versatile estimation techniques, including real-data validation.

Findings

The distribution includes many known lifetime distributions as special cases.

Maximum likelihood and other estimators perform well in simulations.

Real data analysis confirms the distribution's practical usefulness.

Abstract

This article presents a new class of generalized transmuted lifetime distributions which includes a large number of lifetime distributions as sub-family. Several important mathematical quantities such as density function, distribution function, quantile function, moments, moment generating function, stress-strength reliability function, order statistics, R\'enyi and q-entropy, residual and reversed residual life function, and cumulative information generating function are obtained. The methods of maximum likelihood, ordinary least square, weighted least square, Cram\'er-von Mises, Anderson Darling, and Right-tail Anderson Darling are considered to estimate the model parameters in a general way. Further, a well-organized Monte Carlo simulation experiments have been performed to observe the behavior of the estimators. Finally, two real data have also been analyzed to demonstrate the effectiveness of the proposed distribution in real-life modeling.