Description: In this paper, 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. 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.

Description: This is the abstract of the paper Minimum Quadratic Distance Estimators for the Zeta Parametric Family. In this paper, we propose a new estimator, based on quadratic distance, asymptotically fully efficient for parameter values greater than 2 and highly efficient for smaller values, but computationally more appealing than the maximum likelihood estimator we compare its asymptotic variance with that of the moment estimator and an estimator proposed by Seal, based on the ratio of the observed frequencies of the first two classes. We also discuss a goodness-of-fit test and a test to discriminate between the zeta distribution and the Poisson distribution truncated at 0.