Inference for a leptokurtic symmetric family of distributions represented by the difference of two gamma variates
We introduce a family of leptokurtic symmetric distributions represented by the difference of two gamma variates. Properties of this family are discussed. The Laplace, sums of Laplace and normal distributions all arise as special cases of this family. We propose a two-step method for
fitting data to this family. First, we perform a test of symmetry, and second, we estimate the parameters by minimizing the quadratic distance between the real parts of the empirical and theoretical characteristic functions. The quadratic distance estimator obtained is consistent, robust and
asymptotically normally distributed. We develop a statistical test for goodness of fit and introduce a test of normality of the data. A simulation study is provided to illustrate the theory.
Keywords: Laplace distribution; double gamma difference; empirical characteristic function; gamma distribution; goodness of fit; leptokurtic distribution; normality test; parameter estimation; quadratic distance; symmetric distribution; test of symmetry
Document Type: Research Article
Affiliations: Département de Mathématiques et de Statistique,Université de Montréal, C.P. 6128, Succursale Centre-villeMontréal,Québec, CanadaH3C 3J7,
Publication date: 01 November 2012
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