Functions and CALL Routines |
Returns the noncentrality parameter from a chi-square distribution.
-
x
-
is a numeric random variable.
Range: |
x 0 |
-
df
-
is a numeric degrees of freedom parameter.
-
prob
-
is a probability.
The CNONCT function returns the nonnegative
noncentrality parameter from a noncentral chi-square distribution whose parameters
are x, df, and nc. If prob
is greater than the probability from the central chi-square distribution with
the parameters x and df, a root to this problem
does not exist. In this case a missing value is returned. A Newton-type algorithm
is used to find a nonnegative root nc of the equation
![[equation]](images/deqn56.gif)
where
![[equation]](images/deqn57.gif)
where
is the probability from the gamma distribution given by
![[equation]](images/deqn58.gif)
If the algorithm fails to converge to a fixed point,
a missing value is returned.
data work;
x=2;
df=4;
do nc=1 to 3 by .5;
prob=probchi(x,df,nc);
ncc=cnonct(x,df,prob);
output;
end;
run;
proc print;
run;
Computations of the Noncentrality Parameters from the Chi-squared Distribution
OBS x df nc prob ncc
1 2 4 1.0 0.18611 1.0
2 2 4 1.5 0.15592 1.5
3 2 4 2.0 0.13048 2.0
4 2 4 2.5 0.10907 2.5
5 2 4 3.0 0.09109 3.0
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