Basic statistics functions

[dcjones]

statistics.jl looked a little bare, so I've implemented some basic functions.

In this commit:

• order : gives the permutation that puts an array in order (equivalent to the R order function).
• tiedrank : as order but compensate for ties (comparable to the R rank function, or the matlab tiedrank), which is used fequently in rank based statistics.
• weighted_mean : weighted mean---a little trivial, yet useful.
• median : (corrected for even-lengthed arrays)
• var : variance
• mad : median absolute deviance (comparable to mad in matlab and R)
• cov_pearson : pearson covariance
• cor_pearson : pearson correlation
• cov_spearman : spearman covariance
• cor_spearman : spearman correlation
• cov : alias for cov_pearson
• cor : alias for cor_pearson

The correlation/covariance functions each have three forms, making them behave similarly to the R cor/cov functions and matlab corr/cov functions.

1. cor(x, y) : return a single number giving the correlation between two vectors
2. cor(X, Y) : return a matrix C, where C_ij gives correlation between column i in X and column j in Y.
3. cor(X) : equivalent to cor(X, X) (but a bit more efficient).

Next up is to add kendall covariance/correlation, a quantile function, then move on to basic statistical tests (t-test, wilcoxon tests, etc).

[dcjones]

The select function was defined over AbstractVector, so I did the same with median, but there was no need for that it turns out.

[JeffBezanson]

Thank you, this is great!
I made some edits in commit d16acc5; could you double-check that one of us hasn't mixed up R's order() vs. rank()? I think I got it right but it's confusing.
Obviously, we use rank for linear algebra, so what's another good name for that function in the statistics sense?

[dcjones]

I think maybe we both mixed them up. :)

My order was incorrect, yours is correct. But my tiedrank was correct.

They should do two different things: order(x)[1] gives the index of the smallest element, whereas tiedrank(x)[1] gives what place the current first element should be in.

[JeffBezanson]

I assume the fix is to use order(v) instead of invperm(order(v))?