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.

摘要

本文提出了一种识别分布的想法，而不是执行经典的拟合优度测试 (GoFT)。为了识别 k 近邻 (kNN) 规则，被应用。我们将读者的注意力集中在识别正态分布上。文章的主要部分致力于涉及 kNN 规则的分布分类器的计算机实现。GoFT 是保守的。识别分布以模拟和真实数据示例为例。当测试统计量超过相关临界值时，就会发出结论：有理由拒绝$H_0.$接下来呢？识别分布是这个问题的答案。