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  2. Chi-squared distribution - Wikipedia

    en.wikipedia.org/wiki/Chi-squared_distribution

    The chi-squared distribution is obtained as the sum of the squares of k independent, zero-mean, unit-variance Gaussian random variables. Generalizations of this distribution can be obtained by summing the squares of other types of Gaussian random variables. Several such distributions are described below.

  3. Chi-squared test - Wikipedia

    en.wikipedia.org/wiki/Chi-squared_test

    Chi-squared distribution, showing χ2 on the x -axis and p -value (right tail probability) on the y -axis. A chi-squared test (also chi-square or χ2 test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large. In simpler terms, this test is primarily used to examine whether two categorical ...

  4. Pearson's chi-squared test - Wikipedia

    en.wikipedia.org/wiki/Pearson's_chi-squared_test

    The Pearson's chi-squared test statistic is defined as . The p-value of the test statistic is computed either numerically or by looking it up in a table. If the p-value is small enough (usually p < 0.05 by convention), then the null hypothesis is rejected, and we conclude that the observed data does not follow the multinomial distribution.

  5. Reduced chi-squared statistic - Wikipedia

    en.wikipedia.org/wiki/Reduced_chi-squared_statistic

    Reduced chi-squared statistic. 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. [2] [3]

  6. Proofs related to chi-squared distribution - Wikipedia

    en.wikipedia.org/wiki/Proofs_related_to_chi...

    The chi square distribution for k degrees of freedom will then be given by: where is the standard normal distribution and is that elemental shell volume at Q ( x ), which is proportional to the ( k − 1)-dimensional surface in k -space for which. It can be seen that this surface is the surface of a k -dimensional ball or, alternatively, an n ...

  7. Chi distribution - Wikipedia

    en.wikipedia.org/wiki/Chi_distribution

    chi. In probability theory and statistics, the chi distribution is a continuous probability distribution over the non-negative real line. It is the distribution of the positive square root of a sum of squared independent Gaussian random variables. Equivalently, it is the distribution of the Euclidean distance between a multivariate Gaussian ...

  8. Inverse-chi-squared distribution - Wikipedia

    en.wikipedia.org/wiki/Inverse-chi-squared...

    CF. In probability and statistics, the inverse-chi-squared distribution (or inverted-chi-square distribution [1]) is a continuous probability distribution of a positive-valued random variable. It is closely related to the chi-squared distribution. It arises in Bayesian inference, where it can be used as the prior and posterior distribution for ...

  9. List of probability distributions - Wikipedia

    en.wikipedia.org/wiki/List_of_probability...

    The chi distribution. The noncentral chi distribution; The chi-squared distribution, which is the sum of the squares of n independent Gaussian random variables. It is a special case of the Gamma distribution, and it is used in goodness-of-fit tests in statistics. The inverse-chi-squared distribution; The noncentral chi-squared distribution

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