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In assessing whether a given distribution is suited to a data-set, the following tests and their underlying measures of fit can be used: Bayesian information criterion; Kolmogorov–Smirnov test; Cramér–von Mises criterion; Anderson–Darling test; Berk-Jones tests [1] [2] Shapiro–Wilk test; Chi-squared test; Akaike information criterion ...
One measure of goodness of fit is the coefficient of determination, often denoted, R 2. In ordinary least squares with an intercept, it ranges between 0 and 1. However, an R 2 close to 1 does not guarantee that the model fits the data well. For example, if the functional form of the model does not match the data, R 2 can be high despite a poor ...
Pearson's chi-squared test or Pearson's test is a statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance. It is the most widely used of many chi-squared tests (e.g., Yates , likelihood ratio , portmanteau test in time series , etc.) – statistical ...
In statistics, the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation ( MSWD ) in isotopic dating [ 1 ] and variance of unit weight in the context of weighted least squares .
In statistics, the Jarque–Bera test is a goodness-of-fit test of whether sample data have the skewness and kurtosis matching a normal distribution. The test is named after Carlos Jarque and Anil K. Bera. The test statistic is always nonnegative. If it is far from zero, it signals the data do not have a normal distribution.
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In statistics the Cramér–von Mises criterion is a criterion used for judging the goodness of fit of a cumulative distribution function compared to a given empirical distribution function, or for comparing two empirical distributions.
The likelihood-ratio test, also known as Wilks test, [2] is the oldest of the three classical approaches to hypothesis testing, together with the Lagrange multiplier test and the Wald test. [3] In fact, the latter two can be conceptualized as approximations to the likelihood-ratio test, and are asymptotically equivalent.