Returns a quantile from the chi-squared distribution
Category: Quantile
CINV ( p , df < ,nc >)
p
is a numeric probability.
Range: ‰ p <1
df
is a numeric degrees of freedom parameter.
Range: df > 0
nc
is a numeric noncentrality parameter.
Range: nc ‰
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, X 2 has a noncentral chi-square distribution with df =1 and nc = µ 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.
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 Statements | Results |
---|---|
q1=cinv(.95,3); | 7.8147279033 |
a2=cinv(.95,3.5,4.5); | 7.504582117 |