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st: RE: Generate Random Variable Given Percentile Values


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Generate Random Variable Given Percentile Values
Date   Tue, 17 Feb 2009 18:28:03 -0000

These percentiles presumably came from somewhere. Why not sample from
the dataset that produced them? 

On the other hand, if this is all you know, your problem is incompletely
specified. You could do this trivially with 1% at 795, 4% at 1834, etc.
But the resulting very lumpy distribution is unlikely to be what you
want, or so I presume.  

In essence, a certain set of percentiles like this don't define a
distribution uniquely, e.g. they are consistent with very different
behaviour in the far tails. 

Nick 
n.j.cox@durham.ac.uk 

Peter Graven

How do you create a random variable given just the percentile
statistics for a distribution? For example the 1%, 5%, 10%, 25%, 50%,
75,%, 90%, 95%, 99% percentiles are, respectively, 795, 1834, 2172,
2641, 3174, 3822, 4900, 5981, 8522. That is, I would like to create a
variable with this distribution in my dataset.

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