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 p^th 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 95^th percentile from a central chi-square distribution with 3 degrees of freedom. The second statement shows how to find the 95^th 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

CINV Function

Syntax

Required Arguments

p

df

Optional Argument

nc

Details

Example

See Also