Distribution of Mean of the Combinations of a Set.
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For some purpose I found myself generating and analyzing the average of the combinations of a set and when I generated the corresponding histogram I was surprised by its shape.Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.
It should be remembered that the combinations C(m, n) of a set are the number of subsets of a set of m elements taken from n in n.
The number of combinations is calculated with:
This is the very simple code to generate the combinations, calculate their mean and generate the histogram:
m <- 50
n <- 6
COMBINATIONS <- t(as.data.frame(combn(m,n)))
C_M <- apply(COMBINATIONS, 1, mean)
hist_all <-hist(C_M, breaks = length(unique(C_M)), col = “blue”)
But if we change the value of m by:
m <- 50
n <- 4
We obtain the following histogram:
https://github.com/pakinja/Data-R-Value
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