Inverse Monsef Distribution: Statistical Properties, Estimation and Application

This paper introduces a new inverse distribution called the Inverse Monsef Distribution (IMON), which is an extension of the Monsef distribution. Most of the statistical and reliability properties of the proposed distribution are derived. The parameters are estimated using two different methods: the maximum likelihood and Cramér-von Mises methods. The proposed distribution demonstrates excellent flexibility in modeling certain types of lifetime data. To illustrate its effectiveness, three real datasets are analyzed and compared with several well-known distributions. Additionally, the reliability properties of the inverse Monsef distribution are discussed. A simulation study is conducted to evaluate the performance of the parameter estimates.