R help - Sep 2003 - Computing a CDF or many quantiles

Given f, a pdf over a finite interval, is there any existing R function that 
can efficiently tabulate the cumulative distribution function for f, or 
produce all N+1 quantiles of the form i/N?  "Efficiently" here means
better
than doing repeated integrations for each point.

Perhaps approx() or approxfun() can help you create an efficient CDF.

HTH,
Jerome

On September 9, 2003 01:38 pm, Kevin S. Van Horn wrote:
> Content-Length: 417
> Status: R
> X-Status: N
>
> Given f, a pdf over a finite interval, is there any existing R function
> that can efficiently tabulate the cumulative distribution function for
> f, or produce all N+1 quantiles of the form i/N?  "Efficiently"
here
> means better than doing repeated integrations for each point.
>
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> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help

On 09-Sep-03 Kevin S. Van Horn wrote:
> Given f, a pdf over a finite interval, is there any existing R function
> that 
> can efficiently tabulate the cumulative distribution function for f, or
> produce all N+1 quantiles of the form i/N?  "Efficiently" here
means
> better than doing repeated integrations for each point.
If that's all you want to do, then a very straightfoward approach should
be OK. I illustrate with a truncated normal distribution on [-1,1]:

  x <- (-1)+(0.001*(0:2000));pdf<-dnorm(x); pdf<-pdf/(sum(pdf)*0.001)
  CDF<-cumsum(pdf)*0.001
  plot(x,pdf,ylim=c(0,1),type="l");lines(x,CDF)

Quantiles:
  N=10;e<-CDF[1];
  for(i in (0:10)){
      j<-max(which(CDF<=i/N+e));print(c(x[j],CDF[j]))
  }
  [1] -1.0000000000  0.0003543119
  [1] -0.75000000    0.09992753
  [1] -0.5390000     0.1999932
  [1] -0.3500000     0.2999169
  [1] -0.1720000     0.4003052
  [1]  0.0000000     0.5002921
  [1]  0.1720000     0.6002703
  [1]  0.3490000     0.7000831
  [1]  0.5380000     0.8000068
  [1]  0.7490000     0.9000725
  [1]  1             1
(a bit approximate here owing to not adopting a slightly more subtle
 approach to the first step).

Tabulation should be extremely straightforward.

Is this what you mean?

Best wishes,
Ted.


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E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
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Date: 09-Sep-03                                       Time: 23:28:53
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