Re: rician random number
- To: mathgroup at smc.vnet.net
- Subject: [mg15211] Re: rician random number
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Tue, 22 Dec 1998 04:01:41 -0500
- Organization: University of Western Australia
- References: <754u82$jdh@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Tomas Garza wrote:
> I suggest you use an approximate method based on an idea by Paul Abbott:
Two possible improvements to this idea.
[1] For the PDF
In[1]:= PDF[A_, s_][r_] = (r/s^2*BesselI[0, (r*A)/s^2])/E^((A^2 +
r^2)/(2*s^2));
use NDSolve (and dynamic programming) instead of NIntegrate to determine
the CDF:
In[2]:= CDF[A_, s_] := CDF[A, s] = Module[{y},
First[y /. NDSolve[{y'[r] == PDF[A, s][r], y[0] == 0}, y, {r, 0,
10}]]]
[2] From the plot,
In[3]:= cdfplot = Plot[CDF[1, 1][x], {x, 0, 10}, PlotRange -> All];
extract the plotpoints (which takes advantage of the adaptive code built
into Plot):
In[4]:= pts = Cases[cdfplot, Line[{x__}] -> x, Infinity];
and then numerically compute the inverse function using interpolation:
In[5]:= inverseCDF[1,1] = Interpolation[Reverse /@ pts]
In[6]:= Table[inverseCDF[1,1][Random[]], {10}]
Cheers,
Paul
____________________________________________________________________
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia Nedlands WA 6907
mailto:paul at physics.uwa.edu.au AUSTRALIA
http://www.physics.uwa.edu.au/~paul
God IS a weakly left-handed dice player
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