st: RE: how to compare two skewed distributions, or calculate confidence intervals for quantiles of each?

["Newson, Roger B" <r.newson@imperial.ac.uk>]

percentiles or percentile differences (which are a slightly different
thing).

If you want to derive confidence intervals for differences between
percentiles, then a good method might be the percentile bootstrap, with
a suitably large number of replicate samples. In Stata, type

whelp bootstrap

to find about the bootstrap. If instead you prefer to calculate
confidence intervals for percentile differences, then you might use the
program -cendif-, which is part of the -somersd- package, downloadable
from SSC using the -ssc- command in Stata. This calculates robust
confidence intervals for median differences, and for other percentile
differences. The -somersd- package includes a manual -cendif.pdf-, in
which the concepts are explained and demonstrated.

I hope this helps.

Roger


Roger Newson
Lecturer in Medical Statistics
POSTAL ADDRESS:
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute at Imperial College London
St Mary's Campus
Norfolk Place
London W2 1PG
STREET ADDRESS:
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute at Imperial College London
47 Praed Street
Paddington
London W1 1NR
TELEPHONE: (+44) 020 7594 0939
FAX: (+44) 020 7594 0942
EMAIL: r.newson@imperial.ac.uk
WEBSITE: http://www.imperial.ac.uk/nhli/r.newson/
Opinions expressed are those of the author, not of the institution.


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of daniel waxman
Sent: 08 March 2006 19:55
To: statalist@hsphsun2.harvard.edu
Subject: st: how to compare two skewed distributions, or calculate
confidence intervals for quantiles of each?

I'd be appreciative if someone could point me in the right direction:

I am trying to compare two populations with skewed
distributions--queuing
times for real patients, and queuing times for simulated patients (the
output of a discrete event simulation program).  

I am most interested in comparing the 50th, 75th, 90th, and 95th
percentiles
between the real and simulated patients, and am struggling with a way to
describe this.

I have only one set of data for the real patients, but I can generate as
many simulated patients as I want (and thus it is easy to generate
confidence intervals for the simulated patients).  The real and
simulated
patients can sort of be thought of as paired observations, although this
is
not strictly speaking true.

The distribution for the real patients is as follows;

. su q, detail


      Percentiles      Smallest
 1%       2.8125              0
 5%       8.4375              0
10%        11.25              0       Obs                3219
25%       28.125              0       Sum of Wgt.        3219

50%      64.6875                      Mean           131.8957
                        Largest       Std. Dev.      179.5722
75%        157.5       1245.938
90%       326.25       1409.063       Variance       32246.18
95%     492.1875       1513.125       Skewness       2.907777
99%     897.1875       1681.875       Kurtosis       13.70393

How can I calculate confidence intervals for these quantiles, or better
yet,
compare this population to a similarly distributed group (say another
variable q2, with the same number of observations)?   

Many thanks.


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