Recognizing distributions using method of potential functions

Abstract

This article focuses on the idea of recognizing distributions rather than performing classic goodness-of-fit tests (GoFTs). In order to recognize distributions, the method of potential functions (MoPF) is used, focusing the reader’s attention on recognizing the normal distribution. The prevailing part of the article concentrates on the implementation of a classifier of distributions that involves MoPF. Recognizing distributions is supported by numerous examples of simulation and real data examples. GoFTs are conservative. When the test statistics exceeds relevant critical value, there are reasons to reject $H_0.$ What next? The answer is: Recognizing distributions by means of the MoPF.

KEYWORDS:

• Recognizing distribution
• Goodness-of-fit test
• Potential function
• Skewness and excess kurtosis
• Monte Carlo method

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G10

Acknowledgments

The author is grateful to the unknown Referees for their valuable comments that contributed to the improvement of the original version of the paper.