2
$\begingroup$

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.

$\endgroup$
  • 2
    $\begingroup$ Maybe s = CDF[EmpiricalDistribution[r], x]; ? $\endgroup$ – b.gates.you.know.what Mar 13 '18 at 10:13
  • 1
    $\begingroup$ @kglr It seems EmpiricalDistribution immediately deals with the TemporalData in a sensible fashion. $\endgroup$ – gwr Mar 13 '18 at 10:19
  • $\begingroup$ @b.gatessucks this actually worked fine $\endgroup$ – Foad Mar 13 '18 at 10:24
  • 2
    $\begingroup$ @gwr, right. But, in version 9, you need to use EmpiricalDistribution[r["States][[1]]] $\endgroup$ – kglr Mar 13 '18 at 10:33
3
$\begingroup$

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

$\endgroup$
  • $\begingroup$ I get this error Syntax::sntxf: "SeedRandom=" cannot be followed by "[March 13, 2018]". ! $\endgroup$ – Foad Mar 13 '18 at 10:20
  • $\begingroup$ I think I did :) I will try again. $\endgroup$ – Foad Mar 13 '18 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 '18 at 10:39
  • 2
    $\begingroup$ @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 '18 at 10:56

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.