Some Simple Method of Estimation for the Parameters of the Discrete Stable Distribution with the Probability Generating Function

• Published in: Communications in statistics. Simulation and computation Vol. 38; no. 9; pp. 2004 - 2017
• Main Authors: Doray, Louis G., Jiang, Shu Mei, Luong, Andrew
• Format: Journal Article
• Language: English
• Published: Colchester Taylor & Francis Group 01.10.2009; Taylor & Francis
• Subjects: Asymptotic bias; Distribution theory; Exact sciences and technology; Linear inference, regression; Linear regression; Mathematics; Normality; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Probability generating function; Probability theory and stochastic processes; Quadratic distance; Sciences and techniques of general use; Statistics; Truncation; Parameter estimation; Gaussian distribution; Probability generating function; Probability distribution; Normality; Variance; Truncation; Asymptotic bias; Covariance; Discrete distribution; Distribution function; 60E07; Generating function; Covariance analysis; 60E10; Linear regression; Probability; Covariance matrix; Variance analysis; Statistical method; Statistical regression; Unbiased estimation; Distribution tail; Numerical simulation; Quadratic distance; Application
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610910903202089

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.