Some Simple Method of Estimation for the Parameters of the Discrete Stable Distribution with the Probability Generating Function |
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Authors: | Louis G. Doray Shu Mei Jiang Andrew Luong |
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Affiliation: | 1. Département de Mathématiques et de Statistique , Université de Montréal , Montréal , Québec , Canada doray@dms.umontreal.ca;3. Département de Mathématiques et de Statistique , Université de Montréal , Montréal , Québec , Canada;4. école d'actuariat, Université Laval , Québec , Canada |
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Abstract: | In this article, we develop a method to estimate the two parameters of the discrete stable distribution. By minimizing the quadratic distance between transforms of the empirical and theoretical probability generating functions, we obtain estimators simple to calculate, asymptotically unbiased, and normally distributed. We also derive the expression for their variance–covariance matrix. We simulate several samples of discrete stable distributed datasets with different parameters, to analyze the effect of tuncation on the right tail of the distribution. |
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Keywords: | Asymptotic bias Linear regression Normality Probability generating function Quadratic distance Truncation |
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