On a length-biased Birnbaum-Saunders regression model applied to meteorological data

TL;DR

This paper introduces a new length-biased Birnbaum-Saunders regression model tailored for environmental and meteorological data, including derivation of properties, estimation methods, and empirical evaluation.

Contribution

It develops a novel regression model based on the length-biased Birnbaum-Saunders distribution, with new properties, estimation procedures, and validation through simulations and real data.

Findings

Distribution is bimodal with mode as a parameter

Maximum likelihood estimates perform well in simulations

Model effectively applied to meteorological data

Abstract

The length-biased Birnbaum-Saunders distribution is both useful and practical for environmental sciences. In this paper, we initially derive some new properties for the length-biased Birnbaum-Saunders distribution, showing that one of its parameters is the mode and that it is bimodal. We then introduce a new regression model based on this distribution. We implement use the maximum likelihood method for parameter estimation, approach interval estimation and consider three types of residuals. An elaborate Monte Carlo study is carried out for evaluating the performance of the likelihood-based estimates, the confidence intervals and the empirical distribution of the residuals. Finally, we illustrate the proposed regression model with the use of a real meteorological data set.