Moment-based inference for Pearson's quadratic q subfamily of distributions

TL;DR

This paper develops moment estimators for Pearson's quadratic subfamily using Stein-type identities, analyzes their asymptotic properties, and introduces tests for normality and symmetry, validated through simulations.

Contribution

It introduces a novel Stein-type covariance approach for parameter estimation in Pearson's quadratic distributions and derives associated asymptotic distributions.

Findings

Estimators are consistent and asymptotically normal.

Proposed tests outperform existing methods in simulations.

The method provides effective tools for symmetry and normality testing.

Abstract

The author uses a Stein-type covariance identity to obtain moment estimators for the parameters of the quadratic polynomial subfamily of Pearson distributions. The asymptotic distribution of the estimators is obtained, and normality and symmetry tests based on it are provided. Simulation is used to compare the performance of the proposed tests with that of other existing tests for symmetry and normality.