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RE: st: RE: Generating skewed distributions on closed intervals


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: Generating skewed distributions on closed intervals
Date   Thu, 29 Sep 2005 09:53:02 +0100

This really depends to a large degree on the associated
scientific and practical problem, which is not clear
to me. But in principle I strongly support the view 
implied by Maarten Buis: only bounded distributions are 
appropriate for finite intervals. What's more their 
behaviour at their extremes should surely be compatible, 
without jumps and ideally without kinks too, i.e. [10,20] 
should join [20,30]. 

Whatever your problem is, it is difficult to believe
that there is not a literature on it, e.g. in demography, 
actuarial science, population ecology. 

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

Reza C Daniels
 
> I've found a solution to the uniform distribution in the 
> -egen var=seq() 
> from() to()- command.
> 
> Is it not simpler just to try and transform this into the three 
> appropriate normal and skewed distributions than to use the -betaden- 
> set of commands? If so, how? If not, I revert to below.
 
> > I'm not sure I'm getting the intuition behind the code of the beta 
> > density functions -betaden- and -nbetaden-. My reading 
> suggests using 
> > -betaden- for the symmetric ~ about 25, and -nbetaden- for 
> the skewed ~s 
> > about 22.5 & 27.5.
> > 
> > However, when I plug in the numbers I get a single result. 
> Clearly I'm 
> > doing something very wrong. Does this mean I need to 
> calculate a & b & 
> > lambda (shape paramaters in betaden commands) first somehow?

Maarten Buis 

> >> you can have a look at the beta distribution
> >> a normal distribution will never stay within an interval (except 
> >> [minus infinity, plus infinity])

Reza C Daniels

> >> I have a categorical variable for agegroup in 10 year 
> bands (e.g. 20-30
> >> years old). I would like to convert the categorical age 
> variable to a
> >> continuous variable by imposing various distributions on 
> the range of
> >> each interval. I then want to conduct sensitivity analysis to my
> >> distributional assumptions.
> >>
> >> For example: let a = the lower limit and b = upper limit 
> for each age
> >> group (e.g. a= 20 years old, b= 30 years old). Keeping the [20,30]
> >> example, the four distributions I want to examine are:
> >>
> >> 1) Uniformly distributed over [20,30].
> >> 2) Normally distributed on the closed interval [20,30], 
> with mode at 25.
> >> 3) Positively skewed on the closed interval [20,30], with 
> mode at 22.5.
> >> 4) Negatively skewed on the closed interval [20,30], with 
> mode at 27.5.
> >>
> >> I have tried various commands (including -drawnorm-), but 
> am unable to
> >> control my variance to ensure the tails are bounded by 
> [20,30] in the
> >> example above (generically, the interval [a,b]).
> >>
> >> Any suggestions on the code for all four distributions 
> above would be
> >> very much appreciated.

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