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


From   "Maarten Buis" <M.Buis@fsw.vu.nl>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: Generating skewed distributions on closed intervals
Date   Thu, 29 Sep 2005 13:50:30 +0200

There are various skewed distributions to choose from: the lognormal, Chi square, F, gamma. These all have a range from 0 to positive infinity.
A distribution that can be skewed, symmetric or flat depending on its parameters, and remains between a fixed range is the beta distribution.

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Reza C Daniels
Sent: donderdag 29 september 2005 13:29
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: RE: Generating skewed distributions on closed intervals

Hi Maarten,

My problem is exactly one of data coarsening, as explained by Heitjan
and Rubin (JASA, 1991). The exception is that they applied this to
heights and I'm wanting to apply it to age.

I am also aware of the need to multiply impute. However, I wanted the
uniform, normal and skewed distributions first before imputing, so that
once I obtained the multiply imputed estimates, I would have something
to compare them to.

Reza


Maarten Buis wrote:
> Hi Reza,
>
> Will you be using this new age variable as a
> dependent/explained/y-variable or as an
> independent/explanatory/x-variable?
>
> If you are using age as an explained variable you will probably end
> up in survival analysis, and they have good techniques of dealing
> with discrete time, so I see no need to invent something new there.
> See: "An Introduction to Survival Analysis Using Stata" by Mario
> Cleves, William W. Gould, and Roberto Gutierrez available from Stata
> Press.
>
> If you will be using age as an explanatory variable than it is good
> to know that even very coarsely categorized variables often produce
> good estimates. If you still want to do something about the
> categorisation, than you would probably want to do some form of
> multiple imputation. The way to think about it is that there is one
> age distribution, which was chopped up in bits. You don't want to use
> different distributions for each age band, since than you would
> assume a very bumpy overall age distribution. So you would first
> estimate the parameters of this age distribution. Than if you wanted
> to draw an age for a person in category 20-30, you would draw from a
> value this distribution truncated between 20 and 30. You would create
> multiple datasets this way, estimate the regression or whatever other
> parameter of interest for each of these datasets, and the mean of
> these effects would be your estimate controlling for the
> categorisation of age. However, I repeat that this is probably more
> trouble that its worth.
>
> I'd like to be sure that this is what you want, before I spent an
> afternoon writing Stata code for you.
>
> Maarten
>
>
>
> -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Reza C
> Daniels Sent: donderdag 29 september 2005 12:34 To:
> statalist@hsphsun2.harvard.edu Subject: Re: st: RE: Generating skewed
> distributions on closed intervals
>
> Hi Maarten,
>
> I tried this in the following way:
>
> set obs 100 -gen z1=invnorm(uniform())- where z>0 -gen z2=ln(z1)- for
> positively skewed -gen z3=exp(z1)- for negatively skewed
>
> As I'm sure you know, this gives me the correct shape of the
> distributions I'm looking for, but the incorrect range.
>
> So, I still can't solve it.
>
> Thanks anyway, Reza
>
>
> Maarten Buis wrote:
>
>> It reminds me of an ordered probit problem: you have one unobserved
>> distribution, which is being carved up. Only now you also have
>> information about where the cuts are made. This should be solvable.
>> You might want to look at the log normal instead of the normal
>> though, since no one can get, or has ever been, -2 (even with
>> plastic surgery).
>>
>>
>>
>> -----Original Message----- From:
>> owner-statalist@hsphsun2.harvard.edu
>> [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Nick Cox
>> Sent: donderdag 29 september 2005 11:09 To:
>> statalist@hsphsun2.harvard.edu Subject: RE: st: RE: Generating
>> skewed distributions on closed intervals
>>
>> Well, I guess wildly the literature you are unaware of holds better
>> solutions, but that's an empty comment as I don't know what it is.
>> The idea that an age distribution is a bunch of little truncated
>> Gaussians sitting next to each other on a line sounds at best
>> strange to me, but as I said I don't understand what your problem
>> is.
>>
>> Nick n.j.cox@durham.ac.uk
>>
>> Reza C Daniels
>>
>>
>>> 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.
>>
>>
>>>> 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.
>>
>>
>>
>>
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>
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