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Can anyone help me plot this?

log P(X >= x) = alpha logx

x=0.001 + k(0.001)

k= 0, ..., 100

I can't figure out the coding for this.. I've been trying this for a while, and can't seem to figure it out. I believe this is a stable distribution, but the built in function doesn't seem to have x^(alpha) so it's making me extra confused.

Can anyone help me out? Thank you.

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Could you clarify what is the PDF or CDF of your distribution ? –  b.gatessucks Nov 8 '12 at 6:43
Which built in functions have you been using ? –  image_doctor Nov 8 '12 at 7:15
This is all my research professor told me to do.. I'm a bit confused myself as to which to show. BUT I need log P(X >= x) on the y axis and alpha logx on the x axis. –  user4341 Nov 8 '12 at 8:22
I've been trying to use the StableDistribution function, and I don't entirely know what to put in for the other four variables.. That's all my research professor had told me. –  user4341 Nov 8 '12 at 8:23
Welcome to Mathematica.SE! I suggest the following: 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Read the FAQs! 3) When you see good Q&A, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. ALSO, remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign` –  Vitaliy Kaurov Nov 8 '12 at 9:48
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1 Answer

up vote 4 down vote accepted

Define a function

f[x_] := Probability[X > x, X \[Distributed] StableDistribution[1, 1.3, -1, 0, 2]]

Because alpha is not given, lets plot it for a few values of alpha:

ParametricPlot[Evaluate[Log[{x^#, f[x]}] & /@ Range[-1.5, 1.5, .45]], {x, -2, 2}, 
                AspectRatio -> 1, Frame -> True, Axes -> False]

enter image description here

StableDistribution looks like this:

Plot[Evaluate@Table[PDF[StableDistribution[1, 1.3, \[Beta], 0, 2], 
    x], {\[Beta], {-1, 0, 1}}], {x, -12, 12}, Filling -> Axis]

enter image description here

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There are so many different competing definitions of the Stable Distribution in the literature (I am familiar with at least 5 different definitions in standard texts), it is rather fanciful to suggest that the above represents 'the solution' to anything of relevance. It appears the question is deficient. –  wolfies Nov 8 '12 at 12:31
@ColinRose I merely show how to use symbolic Probability function (cool mma feature) to make a plot of log P(X >= x) = alpha log x . The particular distribution is irrelevant. The question is deficient, agree, but the answer isn't. Trying to do my best by what's given, - giving such insights to beginners is not a bad idea. They can addopt approach to any other distribution. I am a bit surprised by the down-vote. –  Vitaliy Kaurov Nov 8 '12 at 17:42
Thank you guys for your help! I really appreciate it. Colin, I was also confused about how I was supposed to go about this. But all my professor said was to plot the given equation above and to play around with the alpha values.. I really appreciate everyone's help though! –  user4341 Nov 8 '12 at 21:16
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