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CINV

Category:

Quantile

Arguments

p

is a numeric probability.

Range:

0 p < 1

df

is a numeric degrees of freedom parameter.

Range:

df> 0

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 and variance 1, X² has a noncentral chi-square distribution with df=1 and nc = ².

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.  

Examples

These statements show how to find the 95^th percentile from a central chi-square distribution with 3 degrees of freedom and 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 Statements	Results
q1=cinv(.95,3);	7.8147279033
a2=cinv(.95,3.5,4.5);	7.504582117

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