Inference in a bimodal Birnbaum–Saunders model

Rodney V. Fonseca and Francisco Cribari-Neto

Mathematics and Computers in Simulation (MATCOM), 2018, vol. 146, issue C, 134-159

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 shows 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.

Keywords: Bimodal Birnbaum–Saunders distribution; Birnbaum–Saunders distribution; Monotone likelihood; Nonnested hypothesis test; Penalized likelihood (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:146:y:2018:i:c:p:134-159

DOI: 10.1016/j.matcom.2017.11.004

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