TNONCT Function

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

Categories:	Mathematical
	CAS

Table of Contents

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

multiline equation line 1 upper P Subscript t Baseline left-parenthesis x vertical-bar d f comma n c right-parenthesis minus p r o b equals 0

The following relationship applies to the preceding equation:

multiline equation line 1 upper P Subscript t Baseline left-parenthesis x vertical-bar d f comma n c right-parenthesis equals StartStartFraction 1 OverOver upper Gamma left-parenthesis StartFraction d f Over 2 EndFraction right-parenthesis EndEndFraction integral Subscript 0 Superscript infinity Baseline v Superscript StartFraction d f Over 2 EndFraction minus 1 Baseline epsilon Superscript negative v Baseline integral Subscript negative infinity Superscript x RootIndex StartRoot StartFraction 2 v Over d f EndFraction EndRoot Baseline epsilon Superscript minus StartFraction left-parenthesis u minus n c right-parenthesis squared Over 2 EndFraction Baseline d u d v

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;

Output from the Computations of the Noncentrality Parameter for the t Distribution

Last updated: March 16, 2017