- #36
EngWiPy
- 1,368
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Is it an error margin in the numerical evaluation of the integral?
Is my integral integrable using Mathematica or is there a fundamental error?
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- Thread starter EngWiPy
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In summary, In order to find the average value of ##\varepsilon(\alpha_1,\,\alpha_2,\,\alpha_3)##, you use the cumulative distribution function (CDF) of X, the derivative with respect to x, and the probability density function (PDF).
- #37
Hawkeye18
- 178
- 62
Can you show the figures? What error do you have?
- #38
EngWiPy
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How to upload a figure from my PC?
- #39
Hawkeye18
- 178
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Upload image to a hosting site (dropbox, google photos, tumblr, flickr, etc) then click to "image" on the toolbar and insert the image url.
- #40
EngWiPy
- 1,368
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It doesn't work. I tried both dropbox and google photos. Isn't it "get a link" that I need to insert here?
- #41
- #42
EngWiPy
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I think Monte-Carlo simulations are accurate, so, I suspect, given that everything else done properly, the accuracy of NIntegrate in Mathematica is the issue. Is there any possible reason and I cannot see it?
- #43
Hawkeye18
- 178
- 62
Monte-Carlo convergence is quite slow, ##C/\sqrt N##, maybe the error is due to that. Also there could be some details that Monte-Carlo misses.
On the other hand how Mathematica does NIntegrate is hidden, it might also introduce some systematic error here.
On the other hand how Mathematica does NIntegrate is hidden, it might also introduce some systematic error here.
- #44
EngWiPy
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I remember using Mathematica to evaluate some numerical integral in my master thesis. There was no difference between the numerical integration and Monte-Carlo simulations then!