[WIP] Add Quantile Calculation

[JackStouffer]

This is a work in progress PR to add quantile calculations to dstats that is born out of dlang/phobos#3592. This is very simplistic ATM and will go through many revisions.

Still need to be implemented:

• R method 1
• R method 2
• R method 3
• R method 4
• R method 5
• R method 6
• R method 7
• R method 8
• R method 9
• Add support for user defined types for all methods
• Write better docs

[John-Colvin]

Awesome, thanks for doing this

[JackStouffer]

I'm having a little trouble parsing the R docs you linked me to, when they say

j = floor(np + m) 

and

g = np + m - j

is np supposed to be n * p, or some other constant? Because np is never defined.

[John-Colvin]

I'm not sure whether what I sent you was the most up-to-date version. This
should be the right one:
http://www.rdocumentation.org/packages/stats/functions/quantile

It seems that it's all written out in mathematical notation instead of in
pseudo-code (or R), so i think np is just n*p
On 24 Sep 2015 17:53, "Jack Stouffer" notifications@github.com wrote:

I'm having a little trouble parsing the R docs you linked me to, when they
say

j = floor(np + m)

and

g = np + m - j

is np supposed to be n * p, or some other constant? Because np is never
defined.

—
Reply to this email directly or view it on GitHub
#11 (comment).

[JackStouffer]

Ok, so I got the first three, which were simple enough. But, I could use some more help with the other methods, as neither the R docs nor the linked scholarly paper define what k is when referring to p[k] and X(k).

I also tried to look at the R source for quantile, but it's practically unreadable.

[John-Colvin]

The original paper those methods come from: https://www.amherst.edu/media/view/129116/original/Sample+Quantiles.pdf

[JackStouffer]

Yeah, I looked at that too, but they don't define it either. It sort of just shows up in paragraph five with no explanation.

[John-Colvin]

To be honest, I'm finding it confusing too...

[John-Colvin]

I would recommend testing some simple quantiles examples in R, it might give you clues as to how to interpret the docs/paper.

[jmh530]

x[k] is the order statistic. That means if you have some data, then x[5] is the 5th smallest number. Assume you have some data, 5, 3, 10, 0, 4, x[1] = 0, x[2] = 3, x[3] = 4, then that means that for type 7 (the default) p[1] = 0 / 4, p[2] = 1 / 4, etc. That means that to get the quantile, you would say that the 25% quantile matches up with k=2, which is 3. To get something like 20% quantile, you do 20% * 0 + (1-20%) * 3 = 2.4, and to get the 40% quantile you do 40% * 3 + (1-40%) * 4 = 3.6

[JackStouffer]

Sorry, I no longer have the time to do this. This is a good start for someone else to pick up, so I hope it eventually gets in.