A new probability model with support on unit interval: Structural properties, regression of bounded response and applications

TL;DR

This paper introduces a generalized Log-Lindley distribution for modeling data on (0, 1), deriving its properties, characterizing it via information measures, and demonstrating its effectiveness in regression models for real-world bounded data.

Contribution

It proposes a new flexible distribution extending Log-Lindley, with properties, characterizations, and practical regression models for bounded responses, validated by real data applications.

Findings

The new distribution fits risk management and health expenditure data better than existing models.

Derived properties and characterizations enhance understanding and applicability.

Regression models based on this distribution outperform Beta and Log-Lindley models.

Abstract

A new distribution on (0, 1), generalized Log-Lindley distribution, is proposed by extending the Log-Lindley distribution. This new distribution is shown to be a weighted Log-Lindley distribution. Important probabilistic and statistical properties have been derived. An interesting characterization of the weighted distribution in terms of Kullback-Liebler distance and weighted entropy has also been obtained. A useful result in insurance for the distorted premium principal is presented and verified with numerical calculations. New regression models for bounded responses based on this distribution and their application is illustrated by considering modeling a real life data on risk management and another data set on outpatient health expenditure in comparison with beta regression and Log-Lindley regression models. Much better fits for both data sets justify the relevance of the new distribution in statistical modeling and analysis. Furthermore this generalization, apart from adding flexibility for modelling, retains the compactness and tractability of statistical quantities required for statistical analysis, which is a feature of the Log-Lindley distribution. Thus, the generalized Log-Lindley distribution should be a useful addition to statistical models for practitioners.