Majorization
tests whether a vector x majorizes another vector y
major(x,y)
x,y |
vectors containing non-negative elements (with same length and same mean) |
even if x and y are comparable (i.e. have same length
and same mean) it is possible that neither x majorizes y nor y majorizes x.
logical. TRUE if x majorizes y (x >=(M) y), FALSE if not.
Marshall / Olkin: Inequalities: Theory of Majorization and Its Applications, New York 1979 (Academic Press)
# generate vectors (of incomes) x <- c(541, 1463, 2445, 3438, 4437, 5401, 6392, 8304, 11904, 22261) y <- c(841, 2063, 2445, 3438, 4437, 5401, 6392, 8304, 11304, 21961) # test whether x majorizes y (TRUE, because y is result of # Pigou-Dalton-transfers) major(x,y)
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