An Extended Generalized Frechet (EGFr) Distribution: Properties and It Applications to Reliability Data

Abstract

This paper introduces a novel Extended Generalized Frechet (EGFr) distribution, a flexible extension of the Frechet distribution. The EGFr incorporates additional parameters that provide enhanced flexibility for modeling diverse data sets, especially those with complex patterns or extreme values. The probability density function of the EGFr is derived from the T-X family of distributions and can be expressed as a linear combination of Frechet densities. We investigate the statistical properties of the EGFr, including moments, quantiles, hazard functions and order statistics. Maximum likelihood estimation is used to estimate the model parameters. Extensive simulations demonstrate the consistency and efficiency of the EGFr in parameter estimation. Real-life applications to reliability datasets demonstrate the superior performance of the EGFr over existing Frechet-based distributions. The EGFr’s ability to accurately capture complex data patterns and provide reliable estimates makes it a valuable tool for researchers and practitioners in the fields of reliability engineering and sciences.