On 03/01/2013 4:50 PM, Cristiano wrote: > 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.
If you only have 10^4 samples, then any estimate of the 10^(-7) quantile is going to have pretty serious estimation error attached to it. Even if you have 10^7 samples, the 10^(-7) quantile is determined by a single observation. I would not put too much stock into that estimate. More to the point, one is tempted to ask *why* you need this tail quantiles. What kind of precision do you require?
>> 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. > > Cristiano >