Recognizing distributions rather than goodness-of-fit testing

Abstract

This article puts forward an idea of recognizing distributions rather than carrying-out classic goodness-of-fit tests (GoFTs). For the purpose of recognizing the k-nearest neighbors (kNN) rule is applied. We focus the reader’s attention on recognizing the normal distribution. The main part of the article is devoted to the computer implementation of a classifier of distributions that involves kNN rule. GoFTs are conservative. Recognizing distributions is exemplified by simulation and real data examples. When the test statistics exceeds relevant critical value then the verdict sounds: there are reasons to reject $H_0.$ And what next? Recognizing distributions is the answer to this question.

Keywords:

• Goodness-of-fit test
• k-nearest neighbors rule
• Monte Carlo method
• Recognizing distribution
• Skewness and excess kurtosis

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 article.