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RE: st: RE: model for fractional data with panel data


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: model for fractional data with panel data
Date   Wed, 7 Nov 2007 13:51:02 -0000

Quite so. The beta-distribution can indeed be U-shaped. Some people
would call that shape bimodal. Others define a mode as a peak with a
tail on either side, so that on such a stricter definition we have in
Maarten's case 
two half-modes. (That doesn't make it unimodal!) 

Maarten buis

--- Maarten buis <maartenbuis@yahoo.co.uk> wrote:
> You can see graphs of such bimodel beta distribution in the example
> below. 

Actually that code contained a minor error in the calculation of the
constant. It does not change the shape, so the message from these
graphs doesn't change, but the correct code is below:

*-------------------- begin example ----------------
/*conventional parameterization*/
twoway function y = betaden(.5, .7, x)

/*alternative parameterization*/
local phi = 1.5
local mu = .5
local constant = exp(lngamma(`phi'))/  ///
(exp(lngamma(`mu'*`phi'))*exp(lngamma((1-`mu')*`phi')))

twoway function y = `constant'* ///
                     x^(`mu'*`phi'-1)* ///
                    (1-x)^((1-`mu')*`phi'-1)
*-------------------- end example ------------------

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