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 <[email protected]> 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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