On scale-mixture Birnbaum-Saunders distributions

Abstract:

We present for the first time a justification on the basis of central limit theorems for the family of life distributions generated from scale-mixture of normals. This family was proposed by Bal-akrishnan et al. (2009) and can be used to accommodate unexpected observations for the usual Birnbaum-Saunders distribution generated from the normal one. The class of scale-mixture of normals includes normal, slash, Student-t, logistic, double-exponential, exponential power and many other distributions. We present a model for the crack extensions where the limiting distribu-tion of total crack extensions is in the class of scale-mixture of normals. Moreover, simple Monte Carlo simulations are reported in order to illustrate the results.

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