TNONCT Function

Returns the value of the noncentrality parameter from the Student's t distribution.

Category:

Mathematical

Syntax

TNONCT(x,df,prob)

Required 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

\begin{matrix} P_{t} (x | d f, n c) - p r o b = 0 \end{matrix}

The following relationship applies to the preceding equation:

\begin{matrix} P_{t} (x | d f, n c) = \frac{1}{Γ (\frac{d f}{2})} \int_{0}^{\infty} v^{\frac{d f}{2} - 1} ε^{- v} \int_{- \infty}^{x \sqrt[]{\frac{2 v}{d f}}} ε^{- \frac{{(u - n c)}^{2}}{2}} d u d v \end{matrix}

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

Example

The following example computes the noncentrality parameter from the t distribution.

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;

Computations of the Noncentrality Parameter from the t Distribution