TNONCT Function

TNONCT Function

Returns the value of the noncentrality parameter from the student's t distribution

Category: Mathematical

Syntax

TNONCT ( x , df , prob )

Arguments

x

• is a numeric random variable.

df

• is a numeric degrees-of-freedom parameter.

• Range: df > 0

prob

• is a probability.

• Range: 0 < prob < 1

Details

The TNONCT function returns the nonnegative noncentrality parameter from a noncentral t distribution whose parameters are x , df , and nc . A Newton-type algorithm is used to find a root nc of the equation

where

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

Example

 data work;     x=2;     df=4;     do nc=1 to 3 by .5;        prob=probt(x,df,nc);        ncc=tnonct(x,df,prob);        output;     end;  run;  proc print;  run; 

Output 4.53: Computations of the Noncentrality Parameter from the t Distribution

 OBS      x     df        nc         prob        ncc   1       2      4       1.0       0.76457       1.0   2       2      4       1.5       0.61893       1.5   3       2      4       2.0       0.45567       2.0   4       2      4       2.5       0.30115       2.5   5       2      4       3.0       0.17702       3.0