Chi-square cumulative distribution function

`p = chi2cdf(x,v)`

p = chi2cdf(x,v,'upper')

`p = chi2cdf(x,v)`

computes
the chi-square cdf at each of the values in `x`

using
the corresponding degrees of freedom in `v`

. `x`

and `v`

can
be vectors, matrices, or multidimensional arrays that have the same
size. The degrees of freedom parameters in `v`

must
be positive integers, and the values in `x`

must
lie on the interval `[0 Inf]`

. A scalar input is
expanded to a constant array with the same dimensions as the other
input.

`p = chi2cdf(x,v,'upper')`

returns
the complement of the chi-square cdf at each value in `x`

,
using an algorithm that more accurately computes the extreme upper
tail probabilities.

The *χ*^{2} cdf
for a given value *x* and degrees-of-freedom *ν* is

$$p=F(x|\nu )={\displaystyle {\int}_{0}^{x}\frac{{t}^{(\nu -2)/2}{e}^{-t/2}}{{2}^{\nu /2}\Gamma (\nu /2)}dt}$$

where Γ( · ) is the Gamma function.

The chi-square density function with *ν* degrees-of-freedom
is the same as the gamma density function with parameters *ν*/2
and 2.

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