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This is somewhere between a comment and an answer, but here's a histogram of your sum distribution: dMix[p_, m1_, m2_, s_] := MixtureDistribution[{p, 1 - p}, {LogNormalDistribution[m1, s], LogNormalDistribution[m2, s]}]; Histogram[ Plus @@ RandomVariate[dMix[0.75, 0.5, -1.5, 0.2], {2, 400000}]] Meanwhile, here is a histogram of one of a typical ...


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I post this for illustrative purposes. For thie particular distribution, there are two issues (i) the complex number can be handled with Chop (ii) the very small variance relative to the ellipical region. In the following I use a standard binormal distribution and use NIntegrate on region: bn = MultinormalDistribution[{0, 0}, IdentityMatrix[2]]; reg3[a_, ...


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Just to illustrate some other ways: As Karsten 7 has noted: Probability[xl < x < xu && yl < y < yu, {x, y} \[Distributed] bvn] yields: 0.39307 You can also specify MultinormalDistribution (noting the second argument is covariance matrix): bvn = MultinormalDistribution[{-3.89764, 1.29137}, {{0.08369444426^2, 0}, {0, ...


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@Simon Woods points out in a comment that: In fact the delay on the initial run is caused by compiling code to provide the Poisson distribution :-) You can look at ImageColorOperationsDumpiImageEffectPoissonNoise to see how it works internally. Now, although PoissonDistribution can't be compiled, there's nothing stopping the use of my own C++ ...


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Since the PDF can be computed in closed form you might have some luck with ProbabilityDistribution and some half-way reasonable starting values. Generate the data... mix[p_, m1_, m2_, s_] := MixtureDistribution[{p, 1 - p}, {NormalDistribution[m1, s], NormalDistribution[m2, s]}]; mixdatSum = Plus @@ RandomVariate[mix[0.75, 0.5, -1.5, 0.2], {2, 100}]; ...


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Somebody could verify my code regarding the theory? To start getting the variance-covariance matrix I followed the code found here: Standard errors for maximum likelihood estimates in FindDistributionParameters And I elimitated the last part (Sqrt[Diagonal[cov]/len]]) as I also want to abtain the covariance matrix, so my code is: covariance[data_, dist_, ...



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