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Re: st: retrieve a continuous distribution from a categorical variable


From   David Hoaglin <dchoaglin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: retrieve a continuous distribution from a categorical variable
Date   Fri, 7 Dec 2012 07:02:24 -0500

Hi, Maria.

Those mortality counts are multiples of 100 (or 50), so they do not
look like an actual sample.

More importantly, you have not included information on the population
from which the mortality counts are a sample.  If others have worked
with samples from the same population (or similar populations),
obtaining data for single years of age, and have shown that a
particular type of distribution provides a good fit to those data, you
could fit that type of distribution to the counts for 5-year
intervals.  Once you have a family of distributions, estimating the
parameters from a set of bin counts is straightforward (I would have
to look for a reference).

In the absence of an established family of distributions, you could
consider fitting a curve to the known points on the cumulative
distribution function --- the cumulative fractions at the bin
boundaries: (45, 400/7000), (50, 850/7000), ..., (85, 6200/7000) ---
for example, by using splines.  From the fitted curve you can then
retrieve estimated counts for single years of age.

I hope this discussion helps.

David Hoaglin

On Fri, Dec 7, 2012 at 6:33 AM, Maria Navarro <maria.statalist@gmail.com> wrote:
> Hi all,
>
> I have a variable (mortality counts, see below) for different age
> ranges (below 45, 45-49, 50-54, 55-59, 60-64, 65-69, 70-74, 75-79,
> 80-84, 85 onwards). I would like to know whether is possible to
> retrieve a continuous distribution of deaths out of this information?
>
> I would appreciate if you could help me with this
> Thanks a lot in advance
>
> Best regards,
> Maria
>
> Age Mortality
> below 45 400
> 45-49 450
> 50-54 500
> 55-59 550
> 60-64 600
> 65-69 700
> 70-74 800
> 75-79 1000
> 80-84 1200
> 85 onwards 800
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