A new univariate continuous distribution with applications in reliability

Abstract

In this article, the odd Lomax Gompertz distribution has been introduced, which is derived by modifying the Gompertz distribution to serve as a baseline model in the odd generalized Lomax distribution. The newly proposed model offers enhanced flexibility and provides a promising alternative for modeling lifetime data. This study seeks to establish a solid theoretical foundation for its application through the exploration of several properties, such as non-central moments, stochastic orderings quantile function, and entropy measure, for the new model. Additionally, by conducting simulation analysis, the performance of the various estimation methods is being assessed, which enables the identification of the most reliable approach for estimating the unknown parameters of the newly developed model. The simulation analysis of the two-risk metrics, namely, value at risk and expected shortfall, revealed the ability of the distribution to capture diverse failure rate patterns, which makes it particularly relevant for assessing financial risks. Finally, the suggested model is practiced to two real-life datasets to provide the compelling evidence of superior flexibility and practical versatility compared to existing models in the literature.