Inference in a bimodal Birnbaum-Saunders model

TL;DR

This paper improves inference methods for the bimodal Birnbaum-Saunders distribution by introducing penalized likelihood estimation and various hypothesis tests, demonstrating enhanced reliability through simulations and real data applications.

Contribution

It proposes a penalized likelihood approach for more reliable maximum likelihood estimation in bimodal Birnbaum-Saunders models and develops hypothesis testing procedures including bootstrap methods.

Findings

Penalized likelihood improves estimation convergence.

Various tests are effective for hypothesis inference.

Simulation and empirical results validate methods.

Abstract

We address the issue of performing inference on the parameters that index a bimodal extension of the Birnbaum-Saunders distribution (BS). We show that maximum likelihood point estimation can be problematic since the standard nonlinear optimization algorithms may fail to converge. To deal with this problem, we penalize the log-likelihood function. The numerical evidence we present show that maximum likelihood estimation based on such penalized function is made considerably more reliable. We also consider hypothesis testing inference based on the penalized log-likelihood function. In particular, we consider likelihood ratio, signed likelihood ratio, score and Wald tests. Bootstrap-based testing inference is also considered. We use a nonnested hypothesis test to distinguish between two bimodal BS laws. We derive analytical corrections to some tests. Monte Carlo simulation results and empirical applications are presented and discussed.