Estimation and Inference in Complex Triparametric Pearson Distributions

Abstract

The complex triparametric Pearson distribution is an extension of the Gaussian hypergeometric probability distribution with complex parameters that provides adequate random models for data originating from different fields. In the present article, relations between moments and probabilities are employed to obtain minimum χ² estimators of the parameters. We compare the asymptotic relative efficiency of these estimators with those obtained by several methods. We also develop a test of hypotheses in selecting a two-parameter family from a three-parameter family of distributions. Finally, some examples are provided to illustrate these methods.

Key Words:

• Discrete distributions
• Estimation
• Hypergeometric function
• Inference
• Minimum χ²
• Pearson's family