MarcumQ and Speeding-up Computations

*To*: mathgroup at smc.vnet.net*Subject*: [mg131379] MarcumQ and Speeding-up Computations*From*: bruce.colletti at gmail.com*Date*: Tue, 16 Jul 2013 05:58:06 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net

Re 9.0.1 under Windows 7. Here I find the expected value of a MarcumQ function over a 3D-domain whose joint probability density function is f. How can I more quickly compute the answer 0.930445? I think the domain causes the long computation time (if I had only one computation, this would be okay--but I have many). I had hoped simulation would give a good estimate but it didn't. I can't figure out how to use Compile with Expectation. My hunch says that any increase in speed will come from using some bizarre fact that applies the MarcumQ function to chi-square tests. I've looked for such results but have come up dry. Any ideas to speed up Mathematica computations? Thanks. Bruce Remove@s; f = ProbabilityDistribution[Piecewise@{{6, x1 + x2 + x3 <= 1}}, {x1, 0, 1}, {x2, 0, 1}, {x3, 0, 1}]; q = {0.1, 0.2, 0.3, 0.4}; t = Array[s, 3]; t = Append[t, 1 - Total@t]; Timing@N@Expectation[ MarcumQ[3/2, Sqrt[ 50 Total@(((q - t)^2)/q)], Sqrt[7.8]], Most@t \[Distributed] f] {555.613162, 0.930445}