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

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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.

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  1. R codes can be obtained from the contact author upon request.


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Note that a pre-print version of this manuscript can be found at The current published article is thus an improved and updated version of that work and should become the key reference relating to that work. The computer program, coded in the R language, is available from the first author upon request. We also thank Alejandro Aybar Flores from Universidad del Pacífico for his help in the Shiny app. The authors thank Joan Gladwyn ( for proofreading this manuscript.

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Correspondence to Luis Benites.

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Benites, L., Maehara, R., Vilca, F. et al. Finite Mixture of Birnbaum–Saunders Distributions Using the k-Bumps Algorithm. J Stat Theory Pract 16, 17 (2022).

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