Finite Mixture of Birnbaum-Saunders distributions using the $k$ bumps algorithm

TL;DR

This paper introduces a finite mixture model of Birnbaum-Saunders distributions with multiple components, utilizing the k-bumps algorithm for initialization, and provides estimation, hypothesis testing, and real data applications.

Contribution

It extends previous work by modeling G components, proves model identifiability, and develops an EM algorithm with k-bumps initialization for flexible multimodal data analysis.

Findings

k-bumps algorithm effectively initializes EM for mixture models

Analytical derivation of the empirical information matrix for standard errors

Simulation and real data analyses demonstrate the method's usefulness

Abstract

Mixture models have received a great deal of attention in statistics due to the wide range of applications found in recent years. This paper discusses a finite mixture model of Birnbaum- Saunders distributions with G components, as an important supplement of the work developed by Balakrishnan et al. (2011), who only considered two components. Our proposal enables the modeling of proper multimodal scenarios with greater flexibility, where the identifiability of the model with G components is proven and an EM-algorithm for the maximum likelihood (ML) estimation of the mixture parameters is developed, in which the k-bumps algorithm is used as an initialization strategy in the EM algorithm. The performance of the k-bumps algorithm as an initialization tool is evaluated through simulation experiments. Moreover, the empirical information matrix is derived analytically to account for standard error, and bootstrap procedures for testing hypotheses about the number of components in the mixture are implemented. Finally, we perform simulation studies and analyze two real datasets to illustrate the usefulness of the proposed method.