dear list,
I would like to have a parametric family of continuous distributions,
say G(theta), indexed by a (vector) parameter theta is.element.of Theta,
with the following properties:
i) all family members have (0,infinity) support
ii) (tractable) density exists (to be able to use it for likelihood
estimation realtively easily)
iii) the family is closed under convolution (or even better, under
linear combination)
in the sense that if: X~G(theta_1), Y~G(theta_2), then (X+Y)~G(theta)
for some theta from Theta
(or even if: X~G(theta_1), Y~G(theta_2), a,b are real constants then
(a.X+b.Y)~G(theta) for some theta from Theta)
Obviously, gamma with a fixed scale parameter can satisfy convolution
closure (but not the closure under lin. combination), what about other
possibilities?
Thanks for any hints.
Best regards
Marek Brabec
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