Gamma distribution parameters

Hi,

I'm trying to understand the theory behind the probability distributions specifically what do the shape and scale parameters for gamma distribution mean. I started off with the following material

http://mathworld.wolfram.com/GammaDistribution.html

It is given that alpha parameter is similar to h (which is a count of poisson events). If this is the case, then why should the value of alpha be between 0 and 1 to indicate a decreasing failure rate? Can't the number of events be any positive value?

Can someone give me pointers to the interpretation of these parameters?

Regards
Prasanth

The time between Poisson events has an exponential distribution, which is a Gamma distribution with \(\displaystyle \alpha = 1\). The exponential distribution has a constant failure rate (lookup the definition of failure rate). By definition, a Gamma distribution with \(\displaystyle \alpha < 1\) has an increasing failure rate, while \(\displaystyle \alpha > 1\) gives a decreasing failure rate.

What does alpha mean in the context of decreasing or increasing failure rate ?