Bayesian and Non-Bayesian Inference for Unit-Exponentiated Half-Logistic Distribution with Data Analysis

Abstract

Unit distributions are typically used in probability theory and statistics to illustrate useful quantities with values between zero and one. In this paper, we investigated an appropriate transformation to propose the unit-exponentiated half-logistic distribution (UEHLD), which is also beneficial for modelling data on the unit interval. This distribution’s mathematical features are supplied, including moments, probability-weighted moments, incomplete moments, various entropy measures, and stress–strength reliability. Using well-known estimation techniques such as the maximum likelihood, maximum product of spacing, and Bayesian inference, the estimators of the parameters relevant to the proposed distribution were determined. A comprehensive simulation analysis is provided to examine the performance of parameter estimation approaches on finite samples. The proposed distribution was realistically applied to data on economic growth and data on the tensile strength of polyester fibers to provide an explanation. Furthermore, the analysis of COVID-19 data from Britain as a medical statistical dataset is provided. The experimental results demonstrate that the suggested UEHLD yields a better comparison with some new unit distributions, as well as other unbounded distributions.

The Gull Alpha Power Lomax distributions: Properties, simulation, and applications to modeling COVID-19 mortality rates

“…In this section, Bayesian inference was used to estimate the GAPL distribution parameters using an informative prior in order to achieve the correct posterior distributions. For more information and examples of the Bayesian estimation method, see [23,[50][51][52][53][54][55].…”

Inference and quantile regression for the unit-exponentiated Lomax distribution

“…In this section, a restriction of the EL distribution in the unit interval is done to introduce a new bounded distribution with support on (0, 1) referring to the UEL distribution. Several extension\ modifications have been done using some transformation, in the present work, a similar exponential transformation is used as provided in References [24][25][26][27][28][29][30][31].…”

“…Furthermore, unit distributions allow extra flexibility throughout the unit interval without introducing new parameters to the fundamental distribution. The following are some of the most important unit distributions with diverse numbers of parameters: log-Lindley distribution [ 22 ], unit-Birnbaum-Saunders distribution [ 23 ], unit-Gompertz distribution [ 24 ], unit-inverse Gaussian distribution [ 25 ], unit-Weibull distribution [ 26 ], unit-Burr-XII distribution [ 27 ], unit-Gamma/Gompertz distribution [ 28 ], unit exponentiated half logistic distribution [ 29 ], unit power Burr X distribution [ 30 ] and unit inverse exponentiated Weibull distribution [ 31 ].…”

An Efficient Stress–Strength Reliability Estimate of the Unit Gompertz Distribution Using Ranked Set Sampling

“…[7]), the unit exponentiated half logistic distribution (see ref. [8]), the unit generalized inverse Weibull distribution (see ref. [9]), the another unit Burr XII distribution (see ref.…”