A weighted inverse exponential distribution: Properties, estimation and applications

In this paper, a new unimodal right-skewed weighted inverse exponential distribution is proposed to further solve the problems related to equipment life and survival analyses. Various mathematical properties are analyzed, including the survival and hazard function, tail area property, quantile function, and order statistics. Moreover, the common entropy of the proposed distribution is discussed and compared to accurately measure the information distribution and uncertainty degree of the proposed distribution. The Bayesian estimation and some common classical estimations, such as the maximum likelihood, Anderson Darling, Cramer-von mises, and Ordinary least squares estimation, are used to estimate and analyze the parameters of the proposed distribution. The Lindley approximation and Markov Chain Monte Carlo method with the Metropolis-Hastings algorithm are used to address the complexity of the Bayesian estimation. Additionally, four numerical evaluation criteria are used to compare and analyze the estimated parameters. Finally, by selecting two real datasets for fitting, the proposed distribution is proven to be more flexible and practical in comparison with other distributions. The analysis clearly shows that the proposed distribution efficiently handles these datasets.