Towards a program
The Students t Distribution, n=degrees of freedom, has the expression:
____F(x) = k(n)*
*INTEGRAL (from -00 to x)(1 + x^2/n) ^ -(n+1)/2
The constant k(n) has the values:
___n________________k(n)
___2_____________0.707106721
___4_____________0.375000000
___6_____________0.255155182
___8_____________0.193349510
__10_____________0.155643354
_etc.
where, for n even,
____k(n)= gamma(u)/(b*gamma(v))
____a = gamma(u=(n+1)/2)) =
____ (u-1)*(u-2)*…*(1/2) * sqrt(pi)
____b = sqrt (pi * n)
____c = gamma (v=n/2) = (n/2-1)!
____licas (Luís A. Afonso)
REM "kstudent"
CLS
PRINT " STUDENT DISTRIBUTION "
: PRINT
PRINT " df K "
DEFDBL A-Z
FOR DF = 2 TO 30 STEP 2
PI = 4 * ATN(1)
PII = SQR(DF * PI)
y = INT(DF / 2)
YY = DF / 2 - y
GS = (DF + 1) / 2 - 1
UV = 1
FOR JI = 0 TO DF
TT = GS - JI
IF TT < 1 THEN GOTO 112
UV = UV * TT
NEXT JI
112 GNUM = UV * SQR(PI)
FOR JU = DF / 2 TO 1 STEP -1
GNUM = GNUM / JU
NEXT JU
PRINT USING " ## #.#########";
DF; GNUM / PII
NEXT DF
END
.
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