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Re: generating random number

  • To: mathgroup at smc.vnet.net
  • Subject: [mg34519] Re: generating random number
  • From: "Raf" <r_a_f at yahoo.it>
  • Date: Fri, 24 May 2002 02:42:37 -0400 (EDT)
  • Organization: [Infostrada]
  • References: <200205210628.CAA07798@smc.vnet.net> <acferi$rmd$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"ester" <Ester.Piedipalumbo at na.infn.it> ha scritto nel messaggio
news:acferi$rmd$1 at smc.vnet.net...
>
>  dear Sirs,
>  my name is Ester Piedipalumbo and I am a post doc at the phisics dep. of
>  Naples University.
>  I would like to know if there is something for generating random number
>  according an arbitary PDF (where arbitrary means that it is not standard,
>  but I know, of cource)
>  Thank a lot
>  best regrds
>  Ester
>
>
>
A solution is Montecarlo method [una soluzione è il metodo Montecarlo]:

a = 1;
myPDF[x_] := x/a^2/E^(x^2/(2*a^2))
Plot[myPDF[x], {x, 0, 5}, PlotRange -> All]
myCDF[x_] = Integrate[myPDF[t], {t, 0, x}]
Plot[myCDF[x], {x, 0, 5}, PlotRange -> All]
inv = x /. Solve[myCDF[x] == y, x][[1]]
Plot[inv, {y, 0, 1}, PlotRange -> All]
numCamp = 1000;
gen = Table[y = Random[]; inv, {numCamp}];
ListPlot[gen]
sor = ({#1[[1]], #1[[2]]/numCamp} & ) /@
    Reverse /@ Transpose[{Range[numCamp], Sort[gen]}];
ListPlot[sor]

Saluti,
Raffaele.



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