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Statistics and Algorithms / Probability Distributions / Chi-Squared |
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Parameters |
Degrees of freedom (\(\nu \)) |
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Kernel |
\(x^{(\nu - 2) / 2}\exp \left( -x / 2 \right) \) |
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Support |
\(\left[ 0,\infty \right) \) |
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Mean |
\(\nu \) |
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Variance |
\(2 \nu \) |
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Main Uses |
Asymptotic distribution. Prior, exact and approximate posterior for the precision (reciprocal of variance) of residuals or other shocks in a model |
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Density Function |
%CHISQRDENSITY(x,nu) is the (non-logged) density with nu degrees of freedom at x. |
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Tail Probability |
%CHISQR(x,nu) returns the probability that a chi-squared with nu degrees of freedom exceeds x. |
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Inverse Tail Probability |
%INVCHISQR(p,nu) returns the critical value for probability p. |
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Random Draws |
%RANCHISQR(nu) draws one or more (depending upon the target) independent chi-squareds with NU degrees of freedom |
Copyright © 2025 Thomas A. Doan