Calculation form 1 for ƒΤ2 distribution. Dr.Funatsu, Pofessor of Meisei university, Tokyo. EMail@Contents of forms@Top page
...
[Input] Degree of freedom n=
Input as a…b. If input bƒa, the values of a and b are exchanged.
E is an index of calculation errors and 0.0001…E…0.01
a= b=
E=
[Output]
Value for calculation a=
Value for calculation b=
Value for calculation E=
Probability density(a)=
Probability density(b)=
Mean of ƒΤ2=
Variance of ƒΤ2=
Mode of ƒΤ2=

Area of ƒΤ2…a(probability A)
  =
Area of aƒƒΤ2…b(probability B)
  =
Area of bƒƒΤ2(probability C)
  =
Total area(A+B+C)=1
Positions of a and b are fixed in the image below, irrespective of input values in the
left column.



.........................................................................To seek b for given C.

Referring value of gamma distribution, n= (possible errors in decimals of lower
position.)
@ƒ‘(n/2)=

When n is large, values may be shown in index style as 3.14e+12.
When probabilities in the left column, values may be shown as 3.14e-12.
Be careful of last place of decimals.


Comparison of calculated values for area b`‡ of the distribution. Errors vary by E. The smaller E is, the
smaller become the errors. Following tables are of the exsamples of errors. (Decimals not roundedj Degree of freedom 1 b=1 b=3 b=5 b=10 b=15 b=20 E=0.01 0.318 0.0830 0.0252 0.001561 0.0001072 0.000007 E=0.001 0.3174 0.08323 0.02535 0.001564 0.0001074 0.000007 E=0.0001 0.3172 0.08326 0.02434 0.001565 0.0001075 0.000007 Degree of freedom 2 b=2 b=5 b=10 b=20 E=0.01 0.368 0.081 0.00672 0.0000455 E=0.001 0.3677 0.0821 0.006736 0.0000454 E=0.0001 0.3678 0.0820 0.006737 0.0000453 Degree of freedom 5 b=5 b=10 b=20 b=30 E=0.01 0.4152 0.0750 0.00125 0.00001478 E=0.001 0.4159 0.07522 0.0012499 0.000014719 E=0.0001 0.4158 0.07523 0.0012496 0.000014715