Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

Chi-square inverse cumulative distribution function

`X = chi2inv(P,V)`

`X = chi2inv(P,V)`

computes
the inverse of the chi-square cdf with degrees of freedom specified
by `V`

for the corresponding probabilities in `P`

. `P`

and `V`

can
be vectors, matrices, or multidimensional arrays that have the same
size. A scalar input is expanded to a constant array with the same
dimensions as the other inputs.

The degrees of freedom parameters in `V`

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

must
lie in the interval [0 1].

The inverse chi-square cdf for a given probability *p* and
ν degrees of freedom is

$$x={F}^{-1}(p|\nu )=\{x:F(x|\nu )=p\}$$

where

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

and Γ( · ) is the Gamma function. Each element of
output `X`

is the value whose cumulative probability
under the chi-square cdf defined by the corresponding degrees of freedom
parameter in `V`

is specified by the corresponding
value in `P`

.

Find a value that exceeds 95% of the samples from a chi-square distribution with 10 degrees of freedom.

x = chi2inv(0.95,10) x = 18.3070

You would observe values greater than 18.3 only 5% of the time by chance.

Was this topic helpful?