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?