Q: pattern and simplify

*To*: mathgroup at smc.vnet.net*Subject*: [mg22271] Q: pattern and simplify*From*: "H. J. Wang" <hjwang at ieas.econ.sinica.edu.tw>*Date*: Mon, 21 Feb 2000 20:00:36 -0500 (EST)*Organization*: Computing Center, Academia Sinica*Sender*: owner-wri-mathgroup at wolfram.com

Hi, I'd like to know how to simply an expression that involves many cumulative distribution functions (CDF) and probability density functions (PDF) of a standard normal variable. In short, how can I make Mathematica recognize the "pattern" of "2*mcdf[x]->mycdf[x]", so that it would automatically substitute, say, "2*mcdf[x^2+1]" by "mycdf[x^2+1]"? I'm using Mathematica 3.0. The expression comes from a partial derivative of a function which has some CDFs and PDFs. The result returned by Mathematica is messy, and I believe the expression can be greatly simplified if Mathematica can recognize the CDF and PDF, and substitute them with appropriate symbols. For example, since a standard normal variable's CDF is "1/2*(1 + Erf[x/Sqrt[2]])", expressions like "1 + Erf[x/Sqrt[2]]" should be substitute with "2*myCDF[x]", for all function forms of x. Similarly, "Exp[-(x^2)/2]" should be substituted with "Sqrt[2 Pi]*myPDF[x]". What I can do now is using something like D[ myfunc[x], x] /.{2*mcdf[x]->mycdf[x], Sqrt[2 Pi]*mpdf[-x]->mypdf[x]} but this works only for literal "x" in the expressions. How can I make Mathematica recognize the "pattern" of "2*mcdf[x]->mycdf[x]", so that it would automatically translate, say, "2*mcdf[x^2+1]" into "mycdf[x^2+1]"? Thanks in advance.