[R] A random number from any distribution?þ

[Bert Gunter]

Questionable. Doesn't this implicitly assumes that the log(stock prices) form an AR(1) series? If so, is this reasonable? And what about the occasional shocks? 

Appropriate simulation of time series like stock prices is a tricky business, I believe. I would question whether your naïve approach is going to capture enough of the real dynamics to give meaningful answers. As I'm far from an expert on this sort of thing, I'll just leave it at that.


Bert Gunter
Genentech Nonclinical Biostatistics

http://devo.gene.com/groups/devo/depts/ncb/home.shtml

 

 


-----Original Message-----
From: ivan popivanov [mailto:ivan.popivanov at hotmail.com] 
Sent: Monday, December 14, 2009 2:27 PM
To: gunter.berton at gene.com; greg.snow at imail.org; r-help at r-project.org
Subject: RE: [R]A random number from any distribution?þ

:) I might be trying to do something stupid so let me try again:

1) I have a large sample - daily percentage movement for a stock
2) I want to generate a synthetic stock which has daily movements from the same distribution as the original

The solution I was planning to implement (following the old post cited) is:

1) Compute the quantiles over the known data
2) Generate a uniformly distributed U in (0,1)
3) Find the quantile corresponding to U
4) Using U's offset from the left end of the quantile, compute the daily movement for the synthetic stock

Below is the function I came up with. Two questions:
1) Is there an existing R function to do that?
2) Is this a sound approach?

Thanks in advance!

rsample = function(s, n, step=0.01)
{
   qs = quantile(s, probs=seq(0, 1, step))

   res = rep(0, n)

   unif = runif(n)

   for(i in 1:n)
   {
      uu = unif[i]

      # find uu's quantile
      qid = ceiling(uu / step)
      qleft = (qid - 1)*step

      # compute the result using uu's offset within the quantile
      res[i] = as.numeric(qs[qid]) + ((uu - qleft)/step)*(as.numeric(qs[qid+1]) - as.numeric(qs[qid]))
   }

   return(res)
}

> From: gunter.berton at gene.com
> To: Greg.Snow at imail.org; ivan.popivanov at hotmail.com; r-help at r-project.org
> Subject: RE: [R]A random number from any distribution?þ
> Date: Mon, 14 Dec 2009 13:04:37 -0800
> 
> Sounds like the poster might be interested in bootstrap sampling ...
> As usual, what's the question of interest?
> 
> Bert Gunter
> Genentech Nonclinical Biostatistics
> 
> 
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Greg Snow
> Sent: Monday, December 14, 2009 12:45 PM
> To: ivan popivanov; r-help at r-project.org
> Subject: Re: [R]A random number from any distribution?‏
> 
> Look at the logspline package for an alternative.
> 
> -- 
> Gregory (Greg) L. Snow Ph.D.
> Statistical Data Center
> Intermountain Healthcare
> greg.snow at imail.org
> 801.408.8111
> 
> 
> > -----Original Message-----
> > From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> > project.org] On Behalf Of ivan popivanov
> > Sent: Saturday, December 12, 2009 7:38 PM
> > To: r-help at r-project.org
> > Subject: [R] A random number from any distribution?‏
> > 
> > 
> > Hello,
> > 
> > I have some data, and I want to generate random numbers following the
> > distribution of this data (in other words, to generate a synthetic data
> > set sharing the same stats as a given data set). Reading an old thread
> > I found the following text:
> > 
> > >If you can compute the quantile function of the distribution (i.e.,
> > the
> > >inverse of the integral of the pdf), then you can use the probability
> > >integral transform: If U is a U(0,1) random variable and Q is the
> > quantile
> > >function of the distribution F, then Q(U) is a random variable
> > distributed
> > >as F.
> > 
> > That sounds good, but is there a quick way to do this in R? Let's say
> > my data is contained in "ee", I can get the quantiles using:
> > 
> > qq = quantile(ee, probs=(0,1,0.25))
> > 0% 25% 50% 75% 100%
> > -0.2573385519 -0.0041451053 0.0004538924 0.0049276991 0.1037823292
> > 
> > Then I "know" how to use the above method to generate Q(U) (by looking
> > up U in the first row, and then mapping it to a number using the second
> > row), but is there an R function that does that? Otherwise I need to
> > write my own to lookup the table.
> > 
> > Thanks in advance,
> > Ivan
> > 
> > _________________________________________________________________
> > 
> > 
> > [[alternative HTML version deleted]]
> > 
> > ______________________________________________
> > R-help at r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide http://www.R-project.org/posting-
> > guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> 
> ______________________________________________
> R-help at r-project.org mailing list
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> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
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