The Transform-Transformer Approach: Unveiling the Odd Transmuted Rayleigh-X Family of Distributions

Abstract

The paper presents a novel class (family) of statistical distributions termed Odd Transmuted Rayleigh-X (OTR-X) that was created through a transform-transformer (T-X) approach. The CDF and PDF of the OTR-X family were derived. The available statistical literature studied earlier highlighted that almost all generalized distributions (in which one or more parameters were added) performed well and have better presentation of data than their counterparts with less number of parameters. This has motivated us to developed new family that is capable of producing new distributions. The research paper also presented a clear mathematical formula for several characteristics of the OTR-X family, such as the ordinary moments, moment generating, quantile, and reliability function. In order to find the estimate of the corresponding parameters of the OTR-X family, the technique of maximum likelihood is used in the study. A new sub-model Odd Transmuted Rayleigh Inversed Exponential Distribution (OTRIED) was generated from the OTR-X class and compared its performance to Transmuted Inversed Exponential Distribution (TIED), Exponential Inversed Exponential Distribution (EIED), and Inversed Exponential Distribution using two different datasets. The results have shown that the proposed distribution out performed its competitors when using two different real-world datasets. Furthermore, the proposed distribution can be practicalized to any skewed dataset.