G01FCF returns the deviate associated with the given lower tail probability of the χ2-distribution with real degrees of freedom, via the routine name.
The deviate,
xp, associated with the lower tail probability
p of the
χ2-distribution with
ν degrees of freedom is defined as the solution to
The required
xp is found by using the relationship between a
χ2-distribution and a gamma distribution, i.e., a
χ2-distribution with
ν degrees of freedom is equal to a gamma distribution with scale parameter
2 and shape parameter
ν/2.
For very large values of
ν, greater than
105, Wilson and Hilferty's normal approximation to the
χ2 is used; see
Kendall and Stuart (1969).
Best D J and Roberts D E (1975) Algorithm AS 91. The percentage points of the
χ2 distribution
Appl. Statist. 24 385–388
Hastings N A J and Peacock J B (1975)
Statistical Distributions Butterworth
Kendall M G and Stuart A (1969)
The Advanced Theory of Statistics (Volume 1) (3rd Edition) Griffin
If on entry
IFAIL=0 or
-1, explanatory error messages are output on the current error message unit (as defined by
X04AAF).
The results should be accurate to five significant digits for most parameter values. Some accuracy is lost for p close to 0.0.
For higher accuracy the relationship described in
Section 3 may be used and a direct call to
G01FFF made.