Goodness-of-Fit Test Based on Arbitrarily Selected Order Statistics

Zhenmin Chen

doi:10.13189/ms.2014.020203

Abstract

Checking whether or not the population distribution, from which a random sample is drawn, is a specified distribution is a popular topic in statistical analysis. Such a problem is usually named as goodness-of-fit test. Numerous research papers have been published in this area. The purpose of this short paper is to provide a goodness-of-fit test statistic which works for many kinds of censored data formed by order statistics. This is an extension of the work presented in Chen and Ye (2009). The method can be used for censoredsamplesthat are commonly used in reliability analysis including left censored data, right censored data and doubly censored data.

Highlights

The goodness-of-fit test has its long history
The χ 2 test (Pearson (1900)), Kolmogorov-Smirnov test (Kolmogorov (1933) and Smirnov (1939)), Cramer-von Mises test (Cramer (1928)),and Anderson-Darling test (Anderson and Darling (1952)) are the statistical testspresented in early papers and are still widely used by statistics practitioners
Many research papers have been published in the area of goodness-of-fit test

Summary

Introduction

The goodness-of-fit test has its long history. The primary goal of the goodness-of-fit test is to check how well a specificstatistical model can fit a given data set. The χ 2 test (Pearson (1900)), Kolmogorov-Smirnov test (Kolmogorov (1933) and Smirnov (1939)), Cramer-von Mises test (Cramer (1928)),and Anderson-Darling test (Anderson and Darling (1952)) are the statistical testspresented in early papers and are still widely used by statistics practitioners. It has been shown in that paper that the power of the proposed test in that paper is higher than some of the existing test statistics in some cases, especially for the case that the alternative distributions are V-shaped distributions. In this short paper, the method used in Chen and Ye (2009) will be extended to censored samples. The new test statistic can be used when only some order statistics are available

Uniformity Test Based on Order Statistics

Test for General Distributions