The Cramer-von Mises test is similar to which other statistical test?

The Cramer-von Mises test is a type of goodness-of-fit test used to determine how well a sample distribution matches a specified distribution. It’s particularly useful in assessing the fit of a distribution based on the empirical distribution function (EDF).

The reason the Kolmogorov-Smirnov test is considered similar to the Cramer-von Mises test is that both are based on the EDF and are designed to compare a sample's distribution to a theoretical distribution. They measure discrepancies between the empirical and theoretical cumulative distribution functions, providing insights into how well the theoretical model fits the observed data.

While the Anderson-Darling test is another goodness-of-fit test, it places higher emphasis on the tails of the distribution, which makes it conceptually distinct from the Cramer-von Mises test. The T-test is a parametric test used for comparing means between groups, which does not align with the purpose of the Cramer-von Mises test. Regression analysis, on the other hand, is a statistical process for estimating relationships among variables and is fundamentally different from both tests that focus on distribution fitting.

By understanding the characteristics of the Cramer-von Mises test and its relationship to the Kolmogorov-Smirnov