Inference and quantile regression for the unit-exponentiated Lomax distribution

In probability theory and statistics, it is customary to employ unit distributions to explain practical variables having values between zero and one. This study suggests a brand-new distribution for modelling data on the unit interval called the unit-exponentiated Lomax (UEL) distribution. The statistical aspects of the UEL distribution are shown. The parameters corresponding to the proposed distribution are estimated using widely recognized estimation techniques, such as Bayesian, maximum product of spacing, and maximum likelihood. The effectiveness of the various estimators is assessed through a simulated scenario. Using mock jurors and food spending data sets, the UEL regression model is demonstrated as an alternative to unit-Weibull regression, beta regression, and the original linear regression models. Using Covid-19 data, the novel model outperforms certain other unit distributions according to different comparison criteria.

Automated summary

A new probability distribution called the unit-exponentiated Lomax (UEL) distribution is proposed for modeling data on the unit interval. The study estimates the parameters of the UEL distribution using Bayesian, maximum product of spacing, and maximum likelihood estimation techniques, and evaluates the performance of various estimators through simulated scenarios. The UEL regression model is demonstrated as an alternative to unit-Weibull regression, beta regression, and linear regression models using mock jurors, food spending, and Covid-19 data, showing superior performance compared to certain other unit distributions.