CNONCT Function

Returns the noncentrality parameter from a chi-squared distribution

Category: Mathematical

Syntax

CNONCT ( x , df , prob )

Arguments

is a numeric random variable.
Range: x ‰

is a numeric degrees of freedom parameter.
Range: df > 0

prob

is a probability.
Range: 0 < prob < 1

Details

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

where

where P _g ( x a ) is the probability from the gamma distribution given by

If the algorithm fails to converge to a fixed point, a missing value is returned.

Examples

 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;

Output 4.18: 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