Calculation form 2 for t-distribution. Dr.Funatsu, Professor of Meisei university, Tokyo.　Mail　Contents of forms　Top page

C and b are fixed in the image below, irrespective of input value of C in the left
column.

..................................................To seek related probabilities for given a and b.

Referring values of gamma- and beta-function n=（possible errors in lower
place of decimals.）
　Γ(n/2)= , Γ(n/2+0.5)= , Β(0.5, n/2)=

When n is large, the values may be shown in index style as 3.14e+20. Be careful
of last place of decimals.

Calculation errors of b Errors vary by E. The smaller E is, the smaller become the errors. Following tables are values for reference.



Degree of freedom n=1, and C=0.025(decimals not rounded)
                   E=0.01       E=0.001       E=0.0001       E=0.00001       Known value
Shown values of b  12.755       12.7065       12.7062        12.7061         12.706

Degree of freedom n=5, and C=0.025(decimals not rounded)
                   E=0.01       E=0.001       E=0.0001       E=0.00001       Known value
Shown values of b  2.575        2.5705        2.5706         2.5705          2.571

Degree of freedom n=1, and E=0.0001(decimals not rounded)
                     C=0.1        C=0.05        C=0.025        C=0.01        C=0.005
Shown values of b    3.0777       6.3137        12.7062        31.8205       63.65705
Known values of b    3.078        6.314         12.706         31.821        63.657

Degree of freedom n=5, and E=0.0001(decimals not rounded)
                     C=0.1        C=0.05        C=0.025        C=0.01        C=0.005
Shown values of b    1.4758       2.0150        2.5706         3.3649        4.0321
Known values of b    1.476        2.015         2.571          3.365         4.032