Hello,
I was looking through the source code of trimmean() and I just realized
that in general it does not remove data evenly from the top and bottom.
Here is the source:
"""
trimmean(x, p)
Compute the trimmed mean of `x`, i.e. the mean after removing a
proportion `p` of its highest- and lowest-valued elements.
"""
function trimmean(x::RealArray, p::Real)
n = length(x)
n > 0 || error("x can not be empty.")
0 <= p < 1 || error("p must be non-negative and less than 1.")
rn = min(round(Int, n * p), n-1)
sx = sort(x)
nl = rn >> 1
nh = (rn - nl)
s = 0.0
for i = (1+nl) : (n-nh)
@inbounds s += sx[i]
end
return s / (n - rn)
end
So this removes `nl` elements from the bottom and `nh` elements from the
top. Some times these are the same number, and some times `nh` is one
higher. This means that some times trimmean() removes values unevenly. This
is not how I have seen the trimmed mean defined. Every source that I know
says that the trimmed mean removes the same number of elements from the top
and bottom. For example, Wilcox (2010) says: "More generally, if we round
[p * n] down to the nearest integer g, remove the g smallest and largest
values and average the n - 2g values that remain". This distinction is not
irrelevant. There are theorems about how to compute the variance and
confidence intervals for the trimmed mean that rely on one particular
definition of the trimmed mean. If you change the definition, I can no
longer compute a confidence interval for the computed value.
Another difference between the trimmean() function and the usual definition
is that the "p% trimmed mean" should mean that you remove p% from the top
and p% from the bottom. Whereas in the trimmean() function it means that
you remove (p/2)% from the top and (p/2)% from the bottom.
Is there any chance that the definition of trimmean() could be changed in a
future release to agree with Wilcox (2010) and other texts?
Cheers,
Daniel.
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