# Gamma Distribution

• Nov 23rd 2008, 11:26 PM
nhabibi
Gamma Distribution
Dear all,

I want to use Gamma distribution. It seems that there must be some constraints on Gamma distribution parameters, because:

1- the probability values in some cases become greater than one!

2-if beta is small and alpha is larges => beta^alpha=0 => probability=Inf

3-if alpah is larges => gamma(alpha)=Inf => probability=NaN

Dose anybody knows the constraints and what I can do in these situations?

Thanks
• Nov 24th 2008, 12:14 AM
mr fantastic
Quote:

Originally Posted by nhabibi
Dear all,

I want to use Gamma distribution. It seems that there must be some constraints on Gamma distribution parameters, because:

1- the probability values in some cases become greater than one!

2-if beta is small and alpha is larges => beta^alpha=0 => probability=Inf

3-if alpah is larges => gamma(alpha)=Inf => probability=NaN

Dose anybody knows the constraints and what I can do in these situations?

Thanks

I would have thought all you need is here: http://en.wikipedia.org/wiki/Gamma_distribution.

I'm not sure where your trouble is. You'll need to be more specific .... exactly what parameter values are causing you trouble?
• Nov 24th 2008, 11:12 PM
nhabibi
Quote:

Originally Posted by mr fantastic
I would have thought all you need is here: Gamma distribution - Wikipedia, the free encyclopedia.

I'm not sure where your trouble is. You'll need to be more specific .... exactly what parameter values are causing you trouble?

Mr. Fantastic,

-When alpha is large => gamma(alpha)=Inf => probaility=NaN
for example: (x=1.5385, alpha=213.958, beta=0.0063)
-If beta is small and alpha is large
for example: (alpha=159, beta=0.0072).
• Nov 25th 2008, 02:35 AM
mr fantastic
Quote:

Originally Posted by nhabibi
Mr. Fantastic,

-When alpha is large => gamma(alpha)=Inf => probaility=NaN
for example: (x=1.5385, alpha=213.958, beta=0.0063)
-If beta is small and alpha is large
for example: (alpha=159, beta=0.0072).

Sorry but I still can't make sense of your problem. What are you trying to do with the gamma distribution?

There is no theoretical problem if $\displaystyle \alpha > 0$ and $\displaystyle \beta > 0$. But if you're using technology to calculate the probabilities, then such values might cause technical problems.