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A Study of the Properties of a New Goodness-of-Fit Test.

Richard Franke, Toke Jayachandran

Open publisher page 1 citations

Abstract

We investigate the power properties of a new goodness-of-fit test proposed by Foutz (1980). This new test is compared with the Chi squared test and the Kolmogorov-Smirnov (K-S) test for normality when the samples come from (i) the family of asymmetric stable distributions, (ii) mixtures of normal distributions, and (iii) the Pearson family. The general conclusion is that the new test performs better than the Chi squared and the K-S test when the parent distribution is heavy-tailed. If the hypothesized distribution differs from the true distribution in location only, the new test does not do as well as the other two.

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What this paper is about

We investigate the power properties of a new goodness-of-fit test proposed by Foutz (1980). This new test is compared with the Chi squared test and the Kolmogorov-Smirnov (K-S) test for normality when the samples come from (i) the family of asymmetric stable distributions, (ii) mixtures of normal distributions, and (iii) the Pearson family. The general conclusion is that the new test performs better than the Chi squared and the K-S test when the parent distribution is heavy-tailed. If the hypothesized distribution differs from the true distribution in location only, the new test does not do as well as the other two.

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Available abstract

We investigate the power properties of a new goodness-of-fit test proposed by Foutz (1980). This new test is compared with the Chi squared test and the Kolmogorov-Smirnov (K-S) test for normality when the samples come from (i) the family of asymmetric stable distributions, (ii) mixtures of normal distributions, and (iii) the Pearson family. The general conclusion is that the new test performs better than the Chi squared and the K-S test when the parent distribution is heavy-tailed. If the hypothesized distribution differs from the true distribution in location only, the new test does not do as well as the other two.

Key concepts: Goodness of fit, Normality test, Pearson's chi-squared test, Kolmogorov–Smirnov test, Anderson–Darling test, Normality, Statistics, Test (biology)

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