Mixture inverse Gaussian distributions and its transformations, moments and applications

N. Balakrishnan, VICTOR ELISEO LEIVA SANCHEZ, Antonio Sanhueza, Enrique Cabrera

Research output: Contribution to journalArticlepeer-review

50 Scopus citations

Abstract

Skewed models are important and necessary when parametric analyses are carried out on data. Mixture distributions produce widely flexible models with good statistical and probabilistic properties, and the mixture inverse Gaussian (MIG) model is one of those. Transformations of the MIG model also create new parametric distributions, which are useful in diverse situations. The aim of this paper is to discuss several aspects of the MIG distribution useful for modelling positive data. We specifically discuss transformations, the derivation of moments, fitting of models, and a shape analysis of the transformations. Finally, real examples from engineering, environment, insurance, and toxicology are presented for illustrating some of the results developed here. Three of the four data sets, which have arisen from the consulting work of the authors, are new and have not been previously analysed. All these examples display that the empirical fit of the MIG distribution to the data is very good.

Original languageEnglish
Pages (from-to)91-104
Number of pages14
JournalStatistics
Volume43
Issue number1
DOIs
StatePublished - 1 Feb 2009

Keywords

  • Goodness-of-fit
  • Kurtosis
  • Lifetime distributions
  • Likelihood methods
  • Skewness

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