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From |
Reza C Daniels <rdaniels@commerce.uct.ac.za> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: RE: Generating skewed distributions on closed intervals |

Date |
Thu, 29 Sep 2005 10:58:19 +0200 |

Thanks Nick,

There is a literature on this problem that I am aware of. I'm just having trouble with the code in Stata to generate my required results.

Reza

Nick Cox wrote:

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 readingsuggests using

-betaden- for the symmetric ~ about 25, and -nbetaden- forthe skewed ~s

about 22.5 & 27.5.Clearly I'm

However, when I plug in the numbers I get a single result.

doing something very wrong. Does this mean I need tocalculate 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 DanielsI have a categorical variable for agegroup in 10 yearbands (e.g. 20-30years old). I would like to convert the categorical agevariable to acontinuous variable by imposing various distributions onthe range ofeach interval. I then want to conduct sensitivity analysis to my

distributional assumptions.

For example: let a = the lower limit and b = upper limitfor each agegroup (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], withmode at 22.5.4) Negatively skewed on the closed interval [20,30], withmode at 27.5.I have tried various commands (including -drawnorm-), butam unable tocontrol my variance to ensure the tails are bounded by[20,30] in theexample above (generically, the interval [a,b]).

Any suggestions on the code for all four distributionsabove would bevery much appreciated.* * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

* * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**RE: st: RE: Generating skewed distributions on closed intervals***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

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