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

 From "Nick Cox" To 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
> 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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