Mathematica Software for Stable Analysis

Needs["StableM7`"]
a={1.5,-1};
stl=Table[{Hue[i],Thickness[0.005]},{i,0.7,1,0.1}];
f2=FSPDF[a,1];
Quiet[Plot[{SCDF[x,a,1],SPDF[x,a,1],StableM7`Private`D1SPDF[x,a,1],D[f2[t],{t,2}]/.t->x},{x,-5,5},
    PlotStyle->stl,PlotRange->All,PerformanceGoal->"Speed"]]

The graphs above a stable distribution {α,  β,  γ,  δ} = {1.5, -1, 1, 0} with its first, second and third derivatives.  In the 1-parameterization δ is the expectation of the distribution.  The probability of a negative outcome is 1/3 and a positive outcome 2/3.  The expected outcome is 0.  There is a probability of an outcome of less than minus ten of 0.0125613, but the probability of an outcome greater than ten is 2.542996641644247`*^-34.  Welcome to the world of stable distributions!

If you would like to work with stable distributions, we recommend the software written by John Nolan, available from Robust Analysis, Inc.  Stable software is available for many platforms, including R, S-Plus, matlab and Mathematica.  The pages on this site as they are updated will be created with the Mathematica version of the software.

txcolor=RGBColor[181/255,18/255,27/255];
t1 = Graphics[Text[Hyperlink[Framed[Style["Financial Home", {txcolor, Bold, Larger}]], "../map/Overview.html"], {-5, 0}]];

t4 = Graphics[Text[Hyperlink[Framed[Style["Robust Analysis, Inc.", {txcolor, Bold, Larger}]], "http://www.robustanalysis.com/"], {0,0}]];
t5 = Graphics[Text[Hyperlink[Framed[Style["Financial Site Index", {txcolor, Bold, Larger}]], "../idx/Index.html"], {5,0}]];
Show[ t1,t4,t5, ImageSize -> 500]
CellPrint[TextCell["\n\n© Copyright " <> ToString[DateList[][[1]]] <> " mathestate    " <> DateString[DateList[], "DateShort"], "Text"]]

© Copyright 2009 mathestate    Tue 4 Aug 2009