This is unclear in several senses.
1. You do not say which commands you used.
2. Telling us your notation tells us little as there
is no standardisation on notation or even parameterisation
for the two-parameter gamma distribution across or within
disciplines. In one common but not universal scheme the
density is given, for variable x >= 0, shape parameter
a > 0 and scale parameter b > 0, by
[1 / (b^a gamma(a))] x^(a - 1) exp(-x / b),
but last time I looked I encountered two other parameterisations
in the literature. This one is what is used by -gammafit- from
SSC.
3. It seems that this cannot be what you used as you
report that your beta was negative.
4. beta * invgammap(alpha, probability) will yield
negative results for negative beta and positive alpha.
5. I don't see that gamma random numbers using your
fitted parameters will tell you anything that your
data cannot, for example in terms of the difference
associated with a covariate, health programme.
6. It sounds as if your variable may be negative.
If I had a variable that looked like a gamma,
apart from being all negative, I would fit
a gamma to absolute values and then re-apply
negation.
7. I don't understand what you mean by
"being Gamma constrained on 0 to 1 interval".
Nick
[email protected]
Carlo Lazzaro
> I have fitted a Gamma distribution with Stata 9/SE from a
> dataset containing
> savings (ie: cost difference all < 0) accrued to patients who
> underwent
> healthcare Programme A (50,000 patients) instead of
> healthcare Programme B
> (50,000 patients)
> Parameter alfa was>0 but beta was less <0.
>
> Then I have drawn 50,000 random samples via InvGamma:
>
> gen InvGamma=beta*invgammap(alfa, uniform())
>
> InvGamma results confirmed that healthcare Programme A was always less
> costly than Healthcare programme B.
> However, being Gamma constrained on 0 to 1 interval, I really
> do not know
> whether the results of InvGamma are or not reliable.
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