7

SeedRandom[1] data = RandomReal[ParetoDistribution[3, 4], {2, 100}]; bwc = BoxWhiskerChart[data, {{"Whiskers", Thick}, {"Outliers", Style["○", Red]}, {"MedianMarker", Directive[Thick, Yellow]}, {"Fences", Thick}}, ChartStyle -> {EdgeForm[{Black,Thickness[.007]}], {RGBColor[{178, 34, 34}/...


5

We can replace NIntegrate by Integrate and use FindRoot. F[x_] := 2*Pi^(-1/2)*Integrate[Exp[-y^2], {y, 0, x}] FindRoot[F[x] == 0.5, {x, 0}] {x -> 0.476936} Another way is again use NDSolve. NDSolve[{F'[x] == 2*Pi^(-1/2)*Exp[-x^2], F[0] == 0, WhenEvent[F[x] == 0.5, {Print[x], "StopIntegration"}]}, F[x], {x, 0, ∞}] 0.476936


2

The short answer is that the covariance matrix is estimated as if there was a single dataset with dummy variables indicating which subset of data belongs to which model. MultiNonlinearModelFit is excellent and very convenient and the only potential issue I have with it is that it makes the unstated assumption that there is a common error variance which I ...


2

I agree, all the forms should result in the same behaviour. That the Switch/Which forms fail for RandomVariate I regard as a bug. The whole point of If,Which and Switch possessing this dual nature of being both control-flow conditionals and potentially functions is that they can be treated like the latter in cases like this. In other words, the purpose of ...


1

This can be done numerically: f[\[Mu]_?NumericQ, \[Sigma]_?NumericQ] := NExpectation[(2 Sqrt[x])/(x + 1) - 1, x \[Distributed] LogNormalDistribution[ (\[Mu] - \[Sigma]^2/2), \[Sigma]]]; f[1, 2] -0.295453


1

A faster option than the one in the comment flushQ[hand_] := MatchQ[hand/100 // Floor, {___, x_, x_, x_, x_, x_, ___}] Count[sortedHands, _?flushQ]/Length[sortedHands] (* 20889/1059380 *)


1

By default, Mathematica appears to use the "MethodOfMoments" method to calculate ARProcess parameters. This is involves calculating the lagged auto-covariances of the input data. However, these are likely calculated by calling the Mathematica "CovarianceFunction" function. The definition given for the covariance calculation (under "...


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