Abstract
Finite mixture model is a widely acknowledged model-based clustering method for analyzing data. In this paper, a new finite mixture model via an extension of Birnbaum-Saunders distribution is introduced. The new mixture model provide a useful generalization of the heavy-tailed lifetime model since the mixing components cover both skewness and kurtosis. Some properties and characteristics of the model are derived and an expectation and maximization (EM)-type algorithm is developed to compute maximum likelihood estimates. The asymptotic standard errors of the parameter estimates are obtained via offering an information-based approach. Finally, the performance of the methodology is illustrated by considering both simulated and real datasets.
Highlights
The Birnbaum–Saunders (BS) distribution [1,2] is a positively skewed and unimodal distribution with non-negative support
In the following theorem, we present a transformational result for the random variable T with SLBS distribution
We have dealt with a new finite mixture model based on a new extension of BS distribution, called the Mix-SLBS
Summary
The Birnbaum–Saunders (BS) distribution [1,2] is a positively skewed and unimodal distribution with non-negative support. Some generalizations and extensions of the BS distribution have been proposed through replacing the standard normal variable Z in (1) by other random variables or replacing φ(⋅) in (2) by other pdfs. For instance by introducing skew-normal distribution and its extensions such as skew-t distribution [9], the related BS versions of them are proposed (see [10,11,12] among others) Another important family of skewed distributions is the class of normal mean-variance (NMV) mixture models [13]. By a simulation study, we show that the proposed model is robust for analyzing heavy tail lifetime data.
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