A novel approach to generate distributions

TL;DR

This paper introduces a new flexible family of distributions with additional parameters, analyzes its mathematical properties, and develops a median-based regression model, validated on real data using maximum likelihood estimation.

Contribution

It presents a novel distribution family with enhanced adaptability and a new regression model based on median reparameterization, implemented in R.

Findings

Distribution family supports positive real line

Regression model effectively captures unimodal data

Model validation shows good fit on real dataset

Abstract

A novel approach to adding two additional parameters to a family of distributions for better adaptability has been put forth. This approach yields a versatile class of distributions supported on the positive real line. We proceed to analyze its mathematical characteristics, such as critical points, modality, stochastic representation, identifiability, quantiles, moments, and truncated moments. We present a new regression model for unimodal continuous data based on a submodel of the newly proposed family of distributions, in which the distribution of the response variable is reparameterized in terms of the median. We use the maximum likelihood method to estimate the parameters, which was implemented through the gamlss package in R. The proposed regression model was applied to a real dataset, and its adequacy was validated through quantile residual analysis.