TY - JOUR

T1 - Finite Mixture of Birnbaum–Saunders Distributions Using the k-Bumps Algorithm

AU - Benites, Luis

AU - Maehara, Rocío

AU - Vilca, Filidor

AU - Marmolejo Ramos, Fernando

PY - 2022/3/9

Y1 - 2022/3/9

N2 - 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 Balakrishnan et al. (J Stat Plann Infer 141:2175–2190, 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.

AB - 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 Balakrishnan et al. (J Stat Plann Infer 141:2175–2190, 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.

UR - https://link.springer.com/article/10.1007/s42519-022-00245-z

M3 - Artículo

SN - 1559-8616

VL - 16

JO - Journal of Statistical Theory and Practice

JF - Journal of Statistical Theory and Practice

ER -