A new class of inverse Gaussian type distributions |
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Authors: | Antonio Sanhueza Víctor Leiva N Balakrishnan |
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Institution: | (1) Department of Mathematics and Statistics, Universidad de La Frontera, Temuco, Chile;(2) Department of Statistics, Universidad de Valparaíso, Casilla 5030, Valparaíso, Chile;(3) Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada |
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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 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. |
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Keywords: | Elliptical distributions Diagnostics Kurtosis Likelihood methods Moments |
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