Definition of Chi-Square Distribution

Definition: The chi-square distribution a continuous distribution, with natural number parameter r. Is the distribution of sums of squares of r standard normal variables. Mean is r, variance is 2r, pdf and cdf is difficult to express in html, and moment-generating function (mgf) is (1-2t)^-r/2.

If n random values z₁, z₂, ..., z_n are drawn from a standard normal distribution, squared, and summed, the resulting statistic is said to have a chi-squared distribution with n degrees of freedom: z₁² + z₂² + ... + z_n²) ~ X²_(n)

This is a one-parameter family of distributions, and the parameter, n, is conventionally labeled the degrees of freedom of the distribution. (Econterms)

Terms related to Chi-Square Distribution:

• Standard normal
• pdf
• cdf

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