Finite mixture of Birnbaum–Saunders distributions using the k-bumps algorithm

Luis Benites, Rocío Maehara, Filidor Vilca, Fernando Marmolejo-Ramos

Research output: Contribution to journalArticle in a journalpeer-review


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.

Original languageEnglish
Article number17
JournalJournal of Statistical Theory and Practice
Issue number2
StatePublished - Jun 2022

Bibliographical note

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© 2022, Grace Scientific Publishing.


  • Birnbaum–Saunders distribution
  • EM algorithm
  • Finite mixture
  • k-bumps algorithm
  • Maximum likelihood estimation


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