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Re: How to calculate quantiles
Posted:
Jan 4, 2013 8:23 AM
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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
>
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