Exponentiated odd Lindley-X family with fitting to reliability and medical data sets

Abstract

This paper concerns constructing a general family of distributions called exponentiated odd Lindley-X (EOL-X) family. We demonstrate that the EOL-X density can be represented as an infinite linear combination of the exponentiated-F densities and, as a result, that many of its mathematical features are derived directly. The fundamental statistical properties, including moments, mean deviations, generating function, order statistics, stochastic ordering, and entropies were investigated. EOL-X special models are introduced. The suggested model presents superior performance when compared to the other models studied, in the reliability and “medical” data. In addition, its bimodal density shape enhances the possibility of good tuning in applications in several other areas, such as survival. Thus, it is expected that this proposal will be of great help to the community studying new families and their adjustments to real data sets.