Chi distribution




Format: Chi(a, b, n)

Uses and Comments

The standardized chi distribution with n degrees of freedom is the distribution followed by the square root of a Chi-Squared(n) random variable:

Chi(0,1,1) is known as a half-normal distribution, i.e.:

The Chi distribution usually appears as the length of a k-dimensional vector whose orthogonal components are independent and normally distributed. The length of the vector will then have a Chi distribution with k degrees of freedom. For example, the Maxwell distribution of (normalized) molecular speeds is a Chi(0,1,3) distribution.

Chi(0,b,2) is the Rayleigh(b) distribution.

ModelRisk functions added to Microsoft Excel for the Chi distribution

VoseChi generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseChiObject constructs a distribution object for this distribution.

VoseChiProb returns the probability density or cumulative distribution function for this distribution.

VoseChiProb10 returns the log10 of the probability density or cumulative distribution function.  

VoseChiFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseChiObject constructs a distribution object of this distribution fitted to data.

VoseChiFitP returns the parameters of this distribution fitted to data.

 

Chi distribution equations

 

 

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