Help with numerical differentiation

*To*: mathgroup at smc.vnet.net*Subject*: [mg80837] Help with numerical differentiation*From*: lederer at ssb.rochester.edu*Date*: Tue, 4 Sep 2007 03:37:37 -0400 (EDT)

I am really confused and stuck at doing this numerical computation. I have searched the archives of this group and tried what was suggested with no solution---Thanks to all in advance. Here is what I am trying to do, elaborated with comments: LPDF[mu_, sigma_, z_] = PDF[LogisticDistribution[mu, sigma], z] UU = U[mu_, sigma_, a_, b_, S_] := NIntegrate[LPDF[mu, sigma, y]*(b ( a + y) + S), {y, -(a + S/b), =E2=88=9E}] - a^2 **defining a function using the logistic distribution and then numerically integrating it over some range... everything seems to work so far** SetSystemOptions["EvaluateNumericalFunctionArgument" -> False] **tried this last statement to get rid of error messages--did not work** maxa[mu_, sigma_, b_, S_] := FindMaximum[U[mu, sigma, a, b, S], {a, 1}] [[1]] ** maximizes U wrt a--this seems to work but with some error messages dealing with non numerical values in the numerical integration** Dmaxasigma[mu_, x_, b_, S_] := D[maxa[mu, x, b, S], x] This is where I am stuck: when I evaluate this function, it does not compute the derivative--just the optimum value of the maximization with a partial derivative sign in front of it. I will need to use this function in a differential equation. Besides this computational problem, any advice on the way to set up these steps so that execution is efficient would be appreciated. This is only part of my entire problem--but cannot proceed without this step. Thanks, Phil in Rochester NY