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I will be running some simulations that involve various density functions, all defined over [0,1]. Once I create the pdf and cdf, I then generate three probability functions, pi0, pi1, and pi2.
The equations used in the optimization involve pi0, pi1, pi2, and the first derivatives of each. But, when I differentiate pi0, pi1, or pi2, I get an expression that involves Sign[q] or Sign[-1+q], or even Sign`[q].
Since q is restricted to be within [0,1], it would be nice if Mathematica could know this and substitute 1 or -1 as appropriate.
For the uniform, this is easy, but for say a truncated normal, it will get messy.
How do I get Mathematica to substitute the proper expression with the domain defined for q, without actually giving a specific value of q?
Attachment: cdfques.nb, URL: ,