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-boun...@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-boun...@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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