A New One Parameter Unit Distribution: Median Based Unit Rayleigh (MBUR): Parametric Quantile Regression Model

TL;DR

This paper introduces the Median Based Unit Rayleigh (MBUR) distribution for parametric quantile regression, detailing estimation, inference, and fit assessment with real data, expanding the statistical modeling toolkit.

Contribution

It presents a novel one-parameter distribution and applies it to parametric quantile regression, including estimation and goodness-of-fit analysis.

Findings

Effective estimation using re-parameterized maximum likelihood

Goodness-of-fit demonstrated with real dataset

Enhanced modeling flexibility with MBUR distribution

Abstract

Parametric quantile regression is illustrated for the one parameter new unit Rayleigh distribution called Median Based Unit Rayleigh distribution (MBUR) distribution. The estimation process using re-parameterized maximum likelihood function is highlighted with real dataset example. The inference and goodness of fit is also explored.