Finite Mixture of Birnbaum-Saunders Distributions Using the K-Bumps Algorithm

• Activity Number: 246 - Data Science
• Type: Contributed
• Date/Time: Wednesday, August 11, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Section on Statistical Computing
• Author(s): Luis Benites* and Rocío Maehara and Filidor Vilca and Fernando Marmolejo-Ramos
• Companies: Pontificia Universidad Católica del Perú and Universidad del Pacífico and Universidade Estadual de Campinas and University of South Australia, Adelaide, Australia
• Keywords: Birnbaum-Saunders distribution; EM algorithm; k-bumps algorithm; Maximum likelihood estimation; Finite Mixture

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, which is an important supplement to that developed by Balakrishnanet al.(2011) who considered a model with two components. Our proposal enables the modeling of proper multimodal scenarios with greater flexibility for a model with two or more components, where a partitional clustering method, named k-bumps, is used as an initialization strategy in the proposed EM algorithm to the maximum likelihood estimates of the mixture parameters. 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 to evaluate the results and analyze two real dataset to illustrate the usefulness of the proposed method.