Functions and CALL Routines

# 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

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.

```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;```

```         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```

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