Development of Topp-Leone Odd Fréchet family of distribution with properties and applications

This paper introduces a novel family of continuous distributions, the Topp-Leone-Odd Fréchet-G family, which is derived by integrating the Odd Fréchet-G family into the Topp-Leone-G distribution. The new distribution demonstrates significant flexibility, making it suitable for modeling datasets with diverse shapes and behaviors. The study examines the basic statistical properties of the distribution, and maximum likelihood estimation (MLE) is used to estimate the model parameters. To demonstrate the practical applicability of the distribution, two real-life datasets were analyzed. The results show that the Topp-Leone-Odd Fréchet-G distribution offers a superior fit compared to competing models, with a reduction in the Akaike Information Criterion (AIC) by 15% and a log-likelihood improvement of 12% compared to the best alternative model. These findings confirm that the proposed distribution provides a more efficient and accurate fit to the datasets, highlighting its potential for broader application in statistical modeling of lifetime and reliability data.