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

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 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.

Automated summary

The length-biased Birnbaum-Saunders distribution is introduced and applied in environmental sciences in this paper. New properties of the distribution are derived, showing that one of its parameters is the mode and that it is bimodal. A new regression model based on this distribution is proposed and parameter estimation is done using the maximum likelihood method. The performance of the proposed methods is evaluated through a Monte Carlo study and illustrated using a real meteorological data set.