On 03/01/2013 21:01, James Waldby wrote: > I think William Elliot either missed the point, or is being purposefully > obtuse to suggest that the phrasing of your question is not correct and > complete in every jot and tittle.
My English is poor, but I hope that it is clear enough. :-)
> Regarding computing those quantiles, I presume the question is which of > the possible interpolation methods to use.
That is the second question. :-) The main problem is that I have just 10^4 to 10^7 samples and I need to calculate the quantile for 10^-7 or lesser and .9999999 or greater.
> Referring to the table at > <http://en.wikipedia.org/wiki/Quantile#Estimating_the_quantiles_of_a_population> > ten methods are shown. When q > N, every one of those methods uses x_1 > as the first q-quantile, and x_N as the last. (q = total number of > quantiles and N = sample size.) > So, in linear time, just find the min and max values in your sample, and > report them as the two desired q-quantiles.
I'm using R-2, SAS-5.
> To do better than that, you need to make assumptions about the distribution.
Unfortunately, the distribution is unknown because it is the A^2 statistic which comes from the Anderson-Darling test.