seeking ref for quantiles/medians
- From: mccolm@xxxxxxxxxxx
- Date: Wed, 27 Jun 2007 12:05:30 -0700
I am looking for a book published at least two years ago, but which
is
hiding from me. So I would like to know if the following probability
(concentration of measure nomenclature) rings any bells.
There is a generalization of the notion of the median, usually
called a "quantile", but in this book called a "median." It is sort
of an inverse of the cumulative distribution function (PDF): if X is
a random variable, F_X (x) = Prob (X <= x). The inverse of this
seems
to have no standard notation, but in this book it is called an e-
median (instead of a quantile), and defined: M_e [X] = inf {x : F_X
(x) > = e}. Notice that this is a perfectly good statistic (like a
variance or an expectation). The book goes on to define the "e-
width"
of X as W_e [X] = M_1-e/2 [X] - M_e/2 [X].
Does this ring any bells? Any suggestions where I might look?
.
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