Integration of norminv function
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Mariia Vasileva on 25 Apr 2017
Is there any way to integrate norminv function for big number of dimensions?
For example in case of 3-dimensional integration integration:
q3 = integral3(fun3,0,1,0,1,0,1);
Matlab returns the following warnings:
Warning: Reached the maximum number of function evaluations (10000). The result passes the global error test.
> In integral2Calc>integral2t (line 136)
In integral2Calc (line 9)
In integral3/innerintegral (line 146)
In integralCalc/iterateScalarValued (line 314)
In integralCalc/vadapt (line 132)
In integralCalc (line 75)
In integral3 (line 121)
In ICDFd (line 20)
Can somebody please give me an advise?
Andrew Newell on 25 Apr 2017
Edited: Andrew Newell on 25 Apr 2017
The problem is that norminv(x,0,1) goes to -Inf as x goes to zero and Inf as x goes to 1 (and ditto for y and z), so it's hard to integrate accurately. If you can manage with a larger tolerance,
q3 = integral3(fun3,0,1,0,1,0,1,'AbsTol',1e-3);
does not return any warnings (the default tolerance is 1e-10). If you need higher precision, you'll just need to be patient, as the warnings are not fatal. However, I don't know if the precision is actually met under such circumstances.