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I'm trying to do triple integration on a bivariate function where one of the upper integration limits is the variable of the outer-most integration. When I execute the following lines, Mathematica takes too long and also returned a not-so-useful answer. This is what I have written so far.

 F[\[Theta]_, \[Alpha]_, \[Beta]_] := CopulaDistribution[{"GumbelHougaard", \[Theta]}, {ExponentialDistribution[\[Alpha]],ExponentialDistribution[\[Beta]]}];
 GumExpExp[x_, s_] := PDF[F[\[Theta], \[Alpha], \[Beta]], {x, s}] //FullSimplify

 M=\[Beta] \!\(\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(T\)]\(\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(s\)]\(\*SubsuperscriptBox[\(\[Integral]\),\(1\), \(10\)]Exp[\(-\[Delta]\)*\\((T - s + u)\)]*x\ GumExpExp[x,u] \[DifferentialD]x \[DifferentialD]u \[DifferentialD]s\)\)\)

And this is what Mathematica returns to me:

NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >> $$ \ \beta \int_0^T\int_0^s\int_0^\infty e^{-\delta (T-s+u)}x GumExpExp[x,u]dxduds\ $$ (with GumExpExp(x,s) replaced by the long expression defined in GumExpExp[x_,s_]).

What is wrong with my function/code? Function GumExpExp (pdf of F) does exist. We may assume values of theta = 1.5, alpha = 0.1, beta = 10, and delta =0.04. I'd like to obtain a numerical answer to this problem.

share|improve this question
    
If You have Set not SetDelayed in definition od Fintx then MMA is trying to caculate general form of integral what is to hard in this case. Later, you can also use NIntegrate to makes it faster: Fintx[s_] := NIntegrate[F[x, s], {x, 0, Infinity}] –  Kuba Jun 4 '13 at 7:38
    
Your box expression is corrupt, and F[x, s] does not exist. Unfortunately, this renders the question ill-posed as it is currently. –  Oleksandr R. Jun 4 '13 at 8:39
    
F is a function of (theta, alpha and beta,) whereas GumExpExp is a function of (x,s). But both exist. I've edited the last 2 lines of the question. I hope it's clearer now. –  SNMRamli Jun 4 '13 at 8:57
    
Okay, that's an improvement. But the box expression is still corrupt, so it's impossible to say what integral you are actually attempting here. Attempts to fix the box expression manually do not result in anything resembling the $\LaTeX$ expression below your code block (you have a stray \[Beta] and the argument of the exponential is different). –  Oleksandr R. Jun 4 '13 at 9:06
1  
Also, check the expression -- you have s in the upper limit of one of the integrals, and you have the same s as a variable of integration ds. How can it be both? –  bill s Jun 4 '13 at 9:18
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