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MarcumQ and Speedingup Computations
Posted:
Jul 16, 2013 5:55 AM


Re 9.0.1 under Windows 7.
Here I find the expected value of a MarcumQ function over a 3Ddomain 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 okaybut 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 chisquare 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}



