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[WP34s] Regularized incomplete Beta function
05-01-2014, 09:08 PM
Post: #5
RE: [WP34s] Regularized incomplete Beta function
(05-01-2014 07:17 PM)Dieter Wrote:  I just tried the regularized incomplete Beta function \(I\beta\) on the 34s. Looking at appendix I of the PDF manual and the given mathematical definition, the argument x and the two parameters a and b of \(I_x(a, b)\) would have to be entered this way:

Z: b
Y: a
X: x


However, this does not work - it throws errors and/or returns wrong results. After some experimenting it turned out that the actual parameter sequence apparently looks like this:

Z: x
Y: b
X: a


Example:
Evaluating \(I_{0.1}(3, 5) = 0.0256915\) requires the sequence 0.1 [ENTER] 5 [ENTER] 3.

Which leads to the question whether the manual or the implementation is wrong. Or... is it me ?-)

Hmmh, let me look at p. 233 (of 244): it clearly states the parameters for Iβ with the respective stack levels. When I compare this definition to Wolfram's definition (see here) I'd derive that their b is our z, their a is our y, and their z is our x. Translating their formula (6) I'd expect e.g.

Iβ(1, 2, 3) = β(2, 3) = 0.083 333
Check: β(2, 3) = Γ(2) Γ(3) / Γ(2+3) = 1! 2! / 4! = 2/24 = 1/12 q.e.d.

This turns out being not the case since Iβ(1, 2, 3) returns a domain error with build 3626. Now let's look whether there's just a permutation error in the parameter sequence of our Iβ:
  • Iβ(3, 1, 2) = domain error
  • Iβ(2, 3, 1) = 1
  • Iβ(1, 3, 2) = domain error
  • Iβ(3, 2, 1) = 1
  • Iβ(2, 1, 3) = domain error
Hmmh, that seems to be a more severe case Sad We'll look into it. Thanks for reporting!

d:-I
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RE: [WP34s] Regularized incomplete Beta function - walter b - 05-01-2014 09:08 PM



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