Yeah, I think that you don't understand me. You suggest:

1 - pnorm(Threshold,mean,sd) = Probability that rnorm(1,mean,sd) > Threshold


I want to know:

Probability that quantile(rnorm(n,mean,sd),prob) > Threshold

I use rnorm() to simulate a sample of size n and then I compute the
statistic from that sample using quantile(). Like all statistics, that
quantile stat (which is a weighted average of 2 order statistics) is a
function of the realized data and hence has a sampling distribution. I want
to compute the cdf of that sampling distribution. Even own the David and
Nagaraja _Order Statistics_ text in my library does not have a closed-form
cdf for that statistic...


On Mon, Feb 14, 2011 at 2:20 PM, Jonathan P Daily <jdaily@usgs.gov> wrote:

> If I understand this, you have a value x, or a vector of values x, and you
> want to know the CDF that this value is drawn from a normal distribution?
>
> I assume you are drawing from rnorm for your simulations, so look at the
> other functions listed when you ?rnorm.
>
> HTH
> --------------------------------------
> Jonathan P. Daily
> Technician - USGS Leetown Science Center
> 11649 Leetown Road
> Kearneysville WV, 25430
> (304) 724-4480
> "Is the room still a room when its empty? Does the room,
>  the thing itself have purpose? Or do we, what's the word... imbue it."
>     - Jubal Early, Firefly
>
> r-help-bounces@r-project.org wrote on 02/14/2011 09:58:09 AM:
>
> > [image removed]
> >
> > [R] CDF of Sample Quantile
> >
> > Bentley Coffey
> >
> > to:
> >
> > r-help
> >
> > 02/14/2011 01:58 PM
> >
> > Sent by:
> >
> > r-help-bounces@r-project.org
> >
> > I need to calculate the probability that a sample quantile will exceed a
> > threshold given the size of the iid sample and the parameters describing
> the
> > distribution of each observation (normal, in my case). I can compute the
> > probability with brute force simulation: simulate a size N sample, apply
> R's
> > quantile() function on it, compare it to the threshold, replicate this
> MANY
> > times, and count the number of times the sample quantile exceeded the
> > threshold (dividing by the total number of replications yields the
> > probability of interest). The problem is that the number of replications
> > required to get sufficient precision (3 digits say) is so HUGE that this
> > takes FOREVER. I have to perform this task so much in my script
> (searching
> > over the sample size and repeated for several different distribution
> > parameters) that it takes too many hours to run.
> >
> > I've searched for pre-existing code to do this in R and haven't found
> > anything. Perhaps I'm missing something. Is anyone aware of an R
> function to
> > compute this probability?
> >
> > I've tried writing my own code using the fact that R's quantile()
> function
> > is a linear combination of 2 order statistics. Basically, I wrote down
> the
> > mathematical form of the joint pdf for the 2 order statistics (a
> function of
> > the sample size and the distribution parameters) then performed a
> > pseudo-Monte Carlo integration (i.e. using Halton Draws rather than R's
> > random draws) over the region where the sample quantile exceeds the
> > threshold. In theory, this should work and it takes about 1000 times
> fewer
> > clock cycles to compute than the Brute Force approach. My problem is
> that
> > there is a significant discrepancy between the results using Brute Force
> and
> > using this more efficient approach that I have coded up. I believe that
> the
> > problem is numerical error but it could be some programming bug;
> regardless,
> > I have been unable to locate the source of this problem and have spent
> over
> > 20 hours trying to identify it this weekend. Please, somebody help!!!
> >
> > So, again, my question: is there code in R for quickly evaluating the
> CDF of
> > a Sample Quantile given the sample size and the parameters governing the
> > distribution of each iid point in the sample?
> >
> > Grateful for any help,
> >
> > Bentley
> >
> >    [[alternative HTML version deleted]]
> >
> > ______________________________________________
> > R-help@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.
>
>

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