G104 Student's t-Distribution and Its Inverse

Function subprogram STUDIS calculates the value of the Student t-distribution function

$F(t,n)\; =\; \{\Gamma (\{12\}(n+1))\pi n\Gamma (\{12\}n)\}\int$_-&inf;^t ( 1+{x²n})^-{12}(n+1)dx

for a given degrees of freedom $n\; \ge 1$ .

Function subprogram STUDIN calculates the inverse $t(F,n)$ .

Structure:

FUNCTION subprogram
User Entry Names: STUDIS, STUDIN
Files Referenced: Printer
External References: GAUSIN (G105), MTLMTR (N002), ABEND (Z035)

Usage:

In any arithmetic expression, STUDIS(T,N) or STUDIN(F,N) has the value $F(T,N)$ or $t(F,N)$ ,

respectively. STUDIS, STUDIN, F and T are of type REAL, N is of type INTEGER.

Error handling:

Error G104.1: $N\; \le 0$ .
Error G104.2: or $F\; >\; 1$ .
In both cases, a message is written on Unit 6, unless subroutine MTLSET (N002) has been called.

Accuracy:

About six decimal places are usually correct. Accuracy is lost for STUDIS when and $N\; >\; 4$ .

Notes:

The subprograms are based on algorithms given in the references.

References:

1. B.E. Cooper, Algorithm AS3 - Applied Statistics 17 (1968) 189.
2. G.W. Hill, Algorithm 396, Student's t-quantiles, Collected algorithms from CACM (1970).

G105