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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. * * 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/

**Follow-Ups**:**Re: st: RE: Generating skewed distributions on closed intervals***From:*Reza C Daniels <rdaniels@commerce.uct.ac.za>

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