Abstract

In the contemporary era, a notable emphasis exists on the practice of generalizing probability distributions, a common approach observed across diverse research domains. This practice entails extending pre-existing baseline probability models to encapsulate and adeptly analyze the intricacies inherent in data. The quadratic transmuted family of distributions, distinguished by its amalgamation of the cumulative distribution function and the quantile function of the base-line distribution. The current study is dedicated to scrutinizing the behaviors exhibited by parameters in the exponential distribution in relation to the quadratic rank transmuted map. Bayesian methodology is the chosen avenue for estimating these parameters, with a deliberate selection of non-informative priors considering symmetric and asymmetric loss functions, facilitating the estimation of the rate and transmuted parameters within the Quadratic Transmuted Exponential Distribution. Since Bayes estimator in closed-form is unfeasible, the study leverages Lindley’s approximation as a computational tool for determining the Bayes estimators through a comprehensive Monte Carlo simulation study, particularly emphasizing evaluating their posterior risks. The study applies these research findings in a practical context by addressing a real-life data application, thereby underscoring the tangible significance and applicability of the research outcomes.

Author: A. Jabarali, Benitta Susan Aniyan and Kumarapandiyan Gnanasegaran

Received on: November, 2023

Accepted on: June, 2024