The long-term inverse Nakagami distribution: Properties, inference and application

In this paper, a new long-term survival distribution, the so-called long-term inverse Nakagami distribution, is presented. The proposed distribution allows us to fit data with unimodal hazard function, where a part of the population is not susceptible to the event of interest, the so-called long-term survival. This distribution can be used, for instance, in clinical studies where a portion of the population can be cured during a treatment. Some mathematical properties of the new distribution are derived. The inferential procedures for the parameters are discussed under the maximum likelihood estimators. A numerical simulation study is carried out to verify the performance of these estimators. Finally, an application to real data on patients’ lifetime after acute myocardial infarction illustrates the usefulness of the proposed distribution.