How do I make the Beta "Subjective" Distribution function work?

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Question:How do I make the Beta "Subjective" Distribution function work?

Posted: NanaP 40 Product: Maple 2023

June 07 2023

Hello community, I am new in this forum and sorry if the following seems rudimentary:

I am replicating a distribution function using Statistics[Distribution] as defined here:

Vose Software's Beta Subjective

I have tested numerically and the function works for this initial values: Min := 3; Mlikely := 8; Avg := 9; Max := 18;

But failed to complete with these values (which I tested works in another software) Min := 1000; Mlikely := 1400; Avg := 1500; Max := 2100;

What puzzles me is the inconsistency of handling the functions (be aware that the server kernel could be slow at times). I hope I don't have to give up and continue my custom distribution project in another software.

Here is the document:

The Beta Subjective Distribution

(1)

(2)

(3)

(4)

f := simplify(piecewise(Min <= x and x <= Max, (x-Min)^(alpha-1)*(Max-x)^(beta-1)/(Beta(alpha, beta)*(Max-Min)^(alpha+beta-1)), 0))

piecewise(x < 3, 0, x <= 18, (4/16875)*(x-3)*(-18+x)^2, 18 < x, 0)

(5)

MD := Distribution(PDF = unapply(f, x), Conditions = [`and`(Min < Mlikely and Mlikely < Max and Min < Avg and Avg < Max and Mlikely <> Avg, piecewise(Avg < Mlikely, Mlikely > Mid, Mid > Mlikely))])