[R] CDF of Sample Quantile

[Jonathan P Daily]

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 at 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 at 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]]
> 
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