R-beta: Quantile function
Peter Dalgaard BSA
p.dalgaard at biostat.ku.dk
Thu Feb 12 13:42:03 CET 1998
Philippe Lambert <phlamber at luc.ac.be> writes:
>
> Is the following behaviour of the quantile function what one would expect?
> > a <- 1:100
> > quantile(a,.6)
> 60%
> 60.4
Yes...
And so is
> quantile(1:10)
0% 25% 50% 75% 100%
1.00 3.25 5.50 7.75 10.00
(Note that *three* values, 8,9,10 fall above the 75% quantile!)
There are many possible definition of quantiles. R's (and Splus's) is
to put 0% at the minimum and 100% at the maximum, and in general, the
k-th smallest is at (k-1)/(n-1), with linear interpolation between the
points. (Try plot(quantile(rnorm(5),seq(0,1,.01))) to see it).
This can surely be criticized, e.g. you'll always have 1 observation
below the 0.00..001 quantile! Alternatives might for example use
(k-.5)/n which puts the smallest observation at 1/2n, but then it's
tricky to define quantiles outside (1/2n,1-1/2n).
--
O__ ---- Peter Dalgaard Blegdamsvej 3
c/ /'_ --- Dept. of Biostatistics 2200 Cph. N
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
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