Gamma and exponential distributions Could someone please clarify for me the support of the gamma distribution? 
According to Wikipedia (and other sources), the gamma distribution is only supported for $x>0$. However, according to Wikipedia again, the exponential distribution is a special case of the gamma distribution with the parameter $k=1$, although the exponential distribution is supported for $x \ge 0$. Does this imply that if the parameter $k$ of the gamma distribution has a certain value, say 1, that its support extends from $x>0$ to $x\ge 0$? 
I would be glad if anyone could clarify this for me.
http://en.wikipedia.org/wiki/Exponential_distribution
http://en.wikipedia.org/wiki/Gamma_distribution
 A: Usually, the support of a distribution is defined to always be a closed set, so in the case of the gamma distribution, $[0,\infty)$. Even if the density function defined by some formula, for some parameter values, then is undefined, that is not a problem. The reason is that density functions are not really functions! Their values at any given point do not give meaning, they have meaning only through being integrated. 
So, in one point of view, densities are equivalence classes of functions, two functions $f, g$ being equivalent if they give the same probabilities (that is, integrals) for all events $A$: $\int_A f(x)\; dx = \int_A g(x)\; dx$ for all events $A$. So the value you assign to the density function at zero do not matter (This is the $L^1$ view.)  See also Can a probability distribution value exceeding 1 be OK?  for discussion. 
Another point of view (leading to the same conclusions) is that densities are differential forms, see Intuitive explanation for density of transformed variable?
