A New Generalization of the Exponentiated Fréchet Distribution with Applications

Abstract

The addition of an extra parameter to standard distributions is a common technique in statistical theory. This study introduces a new generalization of the Exponentiated Fréchet distribution named alpha power exponentiated Fréchet distribution (APEF). The APEF allows for a significant amount of versatility in modeling various data forms as it accommodates upside-down bathtubs, decreasing, and reversed-J shapes for hazard rate function. Some of the APEF’s mathematical properties are derived in close forms. The maximum likelihood technique is used to estimate the new distribution parameters. Numerical results are calculated to demonstrate the estimators’ performance. Five well-known real-life applications show the flexibility and potentiality of the APEF empirically. The APEF outperforms other competing distributions based on model selection criteria.