An Alternative Exponential Model for Skewed Real Data: Characterizations, Bayesian, Non- Bayesian Estimation and Distributional Validation Testing

Abstract

This paper presents a novel exponential model with two parameters, placing particular attention on its practical applications to skewed data as the central area of investigation. The mathematical characteristics of this atypical distribution are established, in a lucid and succinct manner, by the discoveries made in this investigation. Furthermore, it is worth noting that there exist three distinct approaches to describing the distribution. The process of estimating the parameters of the novel model involves employing a range of established methodologies, including the Bayesian technique. When confronted with censored data, the maximum likelihood technique is commonly considered as a viable approach. Pitman's closeness criteria areemployed as the comparative tool when assessing the probability estimate in relation to Bayesian estimation approaches. During the computation of Bayesian estimations, three distinct loss functions, namely generalized quadratic, Linex, and entropy, are employed. A multitude of simulated experiments are conducted to assess the efficacy of various estimation methodologies. The BB algorithm is employed to facilitate the comparison and contrast between the Bayesian technique and the censored maximum likelihood strategy. The Nikulin-Rao-Robson (NKRR) statistic was derived by conducting two empirical studies using real-world data sets characterized by skewed distributions, along with simulation research conducted in an unfiltered environment. Furthermore, this paper delineates two other uses within the same context. The study's findings illustrate the efficacy of the approaches presented for the purposes of distribution and estimation.