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

 From "daniel waxman" To Subject st: how to compare two skewed distributions, or calculate confidence intervals for quantiles of each? Date Wed, 8 Mar 2006 14:54:30 -0500

```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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```