The aim of goodness-of-fit tests is to test if a sample originates from a specific distribution. One of the oldest tests is the goodness-of-fit test (Test 12.2.1). The principle of this test is to divide the sample into classes and compare observed and expected values under the null distribution. The test is suitable for continuous and discrete distributions. However, due to dividing the sample into arbitrary classes the test is not very powerful when testing for a continuous distribution; in this case tests are to be preferred which are customized to specific distributions.
In Chapter 11 we present tests on normality with respect to the outstanding nature of this distribution. Chapter 12 deals with goodness-of-fit tests on distributions other than normal. Most of the tests can be adapted to both cases.
A rough classification of these tests gives two types of goodness-of-fit tests. The first type are tests which employ the empirical distribution function (EDF). Here, the EDF is compared with the theoretical distribution function of the null distribution. One of the famous tests in this class is the Kolmogorov–Smirnov test. The second type are not based on the EDF but compare observed with expected values, such as the above-mentioned -test.