Finite Mixtures of Birnbaum-Saunders Distributions Under a Skew Scale-Mixture Framework

Accepted April 2026

Abstract

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.