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Item type:Publication, Finite mixture of Birnbaum–Saunders distributions using the k-Bumps algorithm(Springer Science and Business Media Deutschland GmbH, 2022-06-01)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. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Regression Modeling of Censored Data Based on Compound Scale Mixtures of Normal Distributions(Brazilian Statistical Association, 2023-06-01)In the framework of censored regression models, the distribution of the error term can depart significantly from normality, for instance, due to the presence of multimodality, skewness and/or atypical observations. In this paper we propose a novel censored linear regression model where the random errors follow a finite mixture of scale mixtures of normal (SMN) distribution. The SMN is an attractive class of symmetrical heavy-tailed densities that includes the normal, Student-t, slash and the contaminated normal distribution as special cases. This approach allows us to model data with great flexibil-ity, accommodating simultaneously multimodality, heavy tails and skewness depending on the structure of the mixture components. We develop an analyt-ically tractable and efficient EM-type algorithm for iteratively computing the maximum likelihood estimates of the parameters, with standard errors and prediction of the censored values as a by-products. The proposed algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of the truncated SMN distributions. The efficacy of the method is verified through the analysis of simulated and real datasets. The methodol-ogy addressed in this paper is implemented in the R package CensMixReg. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Finite Mixtures of Birnbaum-Saunders Distributions Under a Skew Scale-Mixture Framework: Accepted April 2026(2026-04-08)We introduce finite mixtures of Birnbaum–Saunders distributions generated from the scale-mixture-of-skew-normal family (FM–BS–SMSN) to model positive data with asymmetry, multimodality, heterogeneous tails, and latent heterogeneity. The class includes skew-normal, skew-t, skew-slash, and skew-contaminated normal components. Under a common mixing parameter, we establish identifiability of minimal mixtures and, for two components, derive a criterion for strict unimodality. We develop an ECM algorithm and compute standard errors using the outer-product-of-gradients approximation. Simulations show satisfactory finite-sample performance. An application to NHANES BMI data indicates that the FM–BS–ST model provides the best fit, with the BIC favoring two components.1