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

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.

Kumaraswamy Inverted Topp–Leone Distribution with Applications to COVID-19 Data

In this paper, an attempt is made to discover the distribution of COVID-19 spread in different countries such as;Saudi Arabia, Italy, Argentina and Angola by specifying an optimal statistical distribution for analyzing the mortality rate of COVID-19. A new generalization of the recently inverted Topp Leone distribution, called Kumaraswamy inverted Topp–Leone distribution, is proposed by combining the Kumaraswamy-G family and the inverted Topp–Leone distribution. We initially provide a linear representation of its density function. We give some of its structure properties, such as quantile function, median, moments, incomplete moments, Lorenz and Bonferroni curves, entropies measures and stress-strength reliability. Then, Bayesian and maximum likelihood estimators for parameters of the Kumaraswamy inverted Topp–Leone distribution under Type-II censored sample are considered. Bayesian estimator is regarded using symmetric and asymmetric loss functions. As analytical solution is too hard, behaviours of estimates have been done viz Monte Carlo simulation study and some reasonable comparisons have been presented. The outcomes of the simulation study confirmed the efficiencies of obtained estimates as well as yielded the superiority of Bayesian estimate under adequate priors compared to the maximum likelihood estimate. Application to COVID-19 in some countries showed that the new distribution is more appropriate than some other competitive models.