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Statistical Hypothesis Testing with SAS and R by Dirk Taeger, Sonja Kuhnt

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Chapter 12

Tests on other Distributions

In this chapter we present goodness-of-fit tests for distributions other than Gaussian. Tests in Section 12.1 are based on the empirical distribution function (EDF). Section 12.1.1 deals with Pearson's c12-math-0001-test, which is an omnibus test for goodness-of-fit but not so powerful if alternative tests on specific distributions are available.

12.1 Tests based on the EDF

12.1.1 Kolmogorov–Smirnov test

Description: Tests if a sample is sampled from a specific distribution function c12-math-0002.
Assumptions:
  • Data are at least measured on an ordinal scale.
  • The random variables c12-math-0003 are independently distributed with observations c12-math-0004 and a continuous distribution function c12-math-0005.
Hypotheses: (A) c12-math-0006 vs
c12-math-0007 for at least one
(B) vs
with for at least one
(C) vs
with

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