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I use the RandomFunction to generate a continuous random function (trying to model a rough surface):

r = RandomFunction[WienerProcess[0, 1], {0, 10, 0.01}];
ListLinePlot[r, Filling -> Axis, AxesOrigin -> {0, 0}]

enter image description here

I'm able to plot the histogram by:

Histogram[r, 0.2]

enter image description here

But when I try to make a CDF of the data it is empty:

s = CDF[r, x];
Plot[s, {x, -10, 10}, Filling -> Axis]

I would appreciate if you could help me know what is the problem and how I can solve it.

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  • 2
    $\begingroup$ Maybe s = CDF[EmpiricalDistribution[r], x]; ? $\endgroup$
    – b.gates.you.know.what
    Mar 13, 2018 at 10:13
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    $\begingroup$ @kglr It seems EmpiricalDistribution immediately deals with the TemporalData in a sensible fashion. $\endgroup$
    – gwr
    Mar 13, 2018 at 10:19
  • $\begingroup$ @b.gatessucks this actually worked fine $\endgroup$
    – Foad
    Mar 13, 2018 at 10:24
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    $\begingroup$ @gwr, right. But, in version 9, you need to use EmpiricalDistribution[r["States][[1]]] $\endgroup$
    – kglr
    Mar 13, 2018 at 10:33

1 Answer 1

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If what you want is a cumulative distribution function then you will have to make your run data a distribution. You may use EmpiricalDistribution or SmoothKernelDistribution:

SeedRandom = ["March 13, 2018"];
r = RandomFunction[WienerProcess[0, 1], {0, 10, 0.01}];

dist = EmpiricalDistribution @ r;
Plot[ Evaluate@CDF[ dist, x], {x, -10, 10}, 
    Filling -> Axis, 
    PlotRange -> All, PlotPoints -> 1000
]

CDF

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  • $\begingroup$ I get this error Syntax::sntxf: "SeedRandom=" cannot be followed by "[March 13, 2018]". ! $\endgroup$
    – Foad
    Mar 13, 2018 at 10:20
  • $\begingroup$ I think I did :) I will try again. $\endgroup$
    – Foad
    Mar 13, 2018 at 10:22
  • $\begingroup$ If I may ask a side question? How can I integrate over dist now? e.g. f(x)=int[dist,{u,-5,x}] $\endgroup$
    – Foad
    Mar 13, 2018 at 10:39
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    $\begingroup$ @Foad But, that should be exactly what CDF[ dist, x ] will do. Manually you could integrate using PDF[ dist, x] or you could use Probability. $\endgroup$
    – gwr
    Mar 13, 2018 at 10:56

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