On a Modified Weighted Exponential Distribution with Applications

Abstract

Practitioners in all applied domains value simple and adaptable lifetime distributions. They make it possible to create statistical models that are relatively easy to manage. A novel simple lifetime distribution with two parameters is proposed in this article. It is based on a parametric mixture of the exponential and weighted exponential distributions, with a mixture weight depending on a parameter of the involved distribution; no extra parameter is added in this mixture operation. It can also be viewed as a special generalized mixture of two exponential distributions. This decision is based on sound mathematical and physical reasoning; the weight modification allows us to combine some joint properties of the exponential and weighted exponential distribution, which are known as complementary in several modeling aspects. As a result, the proposed distribution may have a decreasing or unimodal probability density function and possess the demanded increasing hazard rate property. Other properties are studied, such as the moments, Bonferroni and Lorenz curves, Rényi entropy, stress-strength reliability, and mean residual life function. Subsequently, a part is devoted to the associated model, which demonstrates how it can be used in a real-world statistical scenario involving data. In this regard, we demonstrate how the estimated model performs well using five different estimation methods and simulated data. The analysis of two data sets demonstrates these excellent results. The new model is compared to the weighted exponential, Weibull, gamma, and generalized exponential models for performance. The obtained comparison results are overwhelmingly in favor of the proposed model according to some standard criteria.