A new class of inverse Gaussian type distributions

Antonio Sanhueza, VICTOR ELISEO LEIVA SANCHEZ, N. Balakrishnan

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

The elliptical laws are a class of symmetrical probability models that include both lighter and heavier tailed distributions. These models may adapt well to the data, even when outliers exist and have other good theoretical properties and application perspectives. In this article, we present a new class of models, which is generated from symmetrical distributions in ℝ and generalize the well known inverse Gaussian distribution. Specifically, the density, distribution function, properties, transformations and moments of this new model are obtained. Also, a graphical analysis of the density is provided. Furthermore, we estimate parameters, propose asymptotic inference and discuss influence diagnostics by using likelihood methods for the new distribution. In particular, we show that the maximum likelihood estimates parameters of the new model under the t kernel are down-weighted for the outliers. Thus, smaller weights are attributed to outlying observations, which produce robust parameter estimates. Finally, an illustrative example with real data shows that the new distribution fits better to the data than some other well known probabilistic models.

Original languageEnglish
Pages (from-to)31-49
Number of pages19
JournalMetrika
Volume68
Issue number1
DOIs
StatePublished - 1 Jun 2008

Keywords

  • Diagnostics
  • Elliptical distributions
  • Kurtosis
  • Likelihood methods
  • Moments

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