# CINV Function

Returns a quantile from the chi-square distribution.

 Category: Quantile

## Syntax

CINV (p,df<,nc> )

### Required Arguments

#### p

is a numeric probability.

 Range 0 ≤ p < 1

#### df

is a numeric degrees of freedom parameter.

 Range df > 0

### Optional Argument

#### nc

is a numeric noncentrality parameter.

 Range nc ≥ 0

## Details

The CINV function returns the pth quantile from the chi-square distribution with degrees of freedom df and a noncentrality parameter nc. The probability that an observation from a chi-square distribution is less than or equal to the returned quantile is p. This function accepts a noninteger degrees of freedom parameter df.
If the optional parameter nc is not specified or has the value 0, the quantile from the central chi-square distribution is returned. The noncentrality parameter nc is defined such that if X is a normal random variable with mean μ and variance 1, X2 has a noncentral chi-square distribution with df=1 and nc = μ2.
CAUTION:
For large values of nc, the algorithm could fail. In that case, a missing value is returned.
Note: CINV is the inverse of the PROBCHI function.

## Example

The first statement following shows how to find the 95th percentile from a central chi-square distribution with 3 degrees of freedom. The second statement shows how to find the 95th percentile from a noncentral chi-square distribution with 3.5 degrees of freedom and a noncentrality parameter equal to 4.5.
SAS Statement
Result
`q1=cinv(.95,3);`
`7.8147279033`
`a2=cinv(.95,3.5,4.5);`
`7.504582117`