Functions and CALL Routines

CNONCT Function

Returns the noncentrality parameter from a chi-square distribution.

Category:

Mathematical

Syntax
Arguments
Details
Examples

Syntax

CNONCT(x,df,prob)

Arguments

x

is a numeric random variable.

Range:

df

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

[equation]

where

[equation]

where [equation] is the probability from the gamma distribution given by

[equation]

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;

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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