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The chi-squared distribution is used in the common chi-squared tests for goodness of fit of an observed distribution to a theoretical one, the independence of two criteria of classification of qualitative data, and in finding the confidence interval for estimating the population standard deviation of a normal distribution from a sample standard ...
Chi-squared distribution, showing χ 2 on the x-axis and p-value (right tail probability) on the y-axis. A chi-squared test (also chi-square or χ 2 test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large.
The chi-squared test, when used with the standard approximation that a chi-squared distribution is applicable, has the following assumptions: [7] Simple random sample The sample data is a random sampling from a fixed distribution or population where every collection of members of the population of the given sample size has an equal probability ...
The chi-square distribution has (k − c) degrees of freedom, where k is the number of non-empty bins and c is the number of estimated parameters (including location and scale parameters and shape parameters) for the distribution plus one. For example, for a 3-parameter Weibull distribution, c = 4.
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 random variable and the origin. The chi distribution describes the positive square roots of a variable obeying a chi-squared distribution.
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
1900: Karl Pearson develops the chi squared test to determine "whether a given form of frequency curve will effectively describe the samples drawn from a given population." Thus the null hypothesis is that a population is described by some distribution predicted by theory.
From this representation, the noncentral chi-squared distribution is seen to be a Poisson-weighted mixture of central chi-squared distributions. Suppose that a random variable J has a Poisson distribution with mean λ / 2 {\displaystyle \lambda /2} , and the conditional distribution of Z given J = i is chi-squared with k + 2 i degrees of freedom.