improving speed of simulation using random numbers

*To*: mathgroup at smc.vnet.net*Subject*: [mg128662] improving speed of simulation using random numbers*From*: felipe.benguria at gmail.com*Date*: Thu, 15 Nov 2012 03:56:34 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

Dear all, I am trying to compute an expected value using simulation. I have a random number x with density function d[x]. I want to compute the expected value of function f[x], which is equal to the integral of f[x] times d[x] over x. In my case, it is difficult to compute the integral so I simulate N values for x and compute the average of f[x] over all N simulated values. My problem is that my code takes to long for my purposes: this is a part of a larger program and is making it unfeasible in terms of time. The following code provides an example of the situation, and my question is how could I reduce the time this takes. THanks a lot for your help g[x_]:= x^2 mydensity[myparameter_]:= ProbabilityDistribution[myparameter*(t)^(-myparameter - 1), {t, 1, Infinity}] randomnum[myparameter_] := RandomVariate[draw[myparameter], 50] Timing[Sum[g[randomnum[5][[i]]], {i, 1, 50}]] Out[1353]= {0.64, 81.7808} This takes 0.6 seconds in my computer and that is way too long for my full program ( I do this many times). Thanks again, Felipe

**Follow-Ups**:**Re: improving speed of simulation using random numbers***From:*Peter Klamser <klamser@googlemail.com>