Wednesday, March 08, 2006

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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