A goodness-of-fit test for the Birnbaum-Saunders distribution based on the probability plot

TL;DR

This paper introduces a new goodness-of-fit test for the Birnbaum-Saunders distribution using the probability plot and sample correlation coefficient, supported by Monte Carlo simulations for critical value determination.

Contribution

It develops a novel goodness-of-fit test based on the probability plot correlation coefficient and provides a method to determine significance levels via Monte Carlo simulations.

Findings

The test effectively assesses the fit of the Birnbaum-Saunders distribution.

Monte Carlo simulations enable accurate critical value estimation.

Application to real data demonstrates practical utility.

Abstract

In the present paper, we develop a new goodness-of-fit test for the Birnbaum- Saunders distribution based on the probability plot. We utilize the sample correlation coefficient from the Birnbaum-Saunders probability plot as a measure of goodness of fit. Unfortunately, it is impossible or extremely difficult to obtain an explicit distribution of this sample correlation coefficient. To address this challenge, we employ extensive Monte Carlo simulations to obtain the empirical distribution of the sample correlation coefficient from the Birnbaum-Saunders probability plot. This empirical distribution allows us to determine the critical values alongside their corresponding significance levels, thus facilitating the computation of the p-value when the sample correlation coefficient is obtained. Finally, two real-data examples are provided for illustrative purposes.