The gamma is a 2-parameter continuous distribution for 0 < y < infinity. Generally, it is used for right-skewed distributions (a special case is the 1-parameter exponential distribution). In principle, it would not be used for counts, which are discrete. The Poisson and negative binomial are two common and popular distributions for count data. However, these distributions can be problematic when the counts are very large. For example, with bacterial cell counts, one might have values such as 10^4, 10^5, 10^8, and so on. In principle, every value from 0 to 10^8 is possible with a discrete distribution, but you can see the problem in dealing with this as a discrete random variable. Thus, as an approximation, the gamma (or log-normal or Weibull) is often used as an approximation of the discrete distribution when there are very large counts or the range of counts is very large. The gamma has the desirable property that the variance is a function of the mean, which is one of the properties of typical discrete distributions.
Be careful when using the gamma: it is defined only for values of y larger than 0. If you have any zeros, they become missing values in the analysis (something you probably don't want). There are more general versions of the gamma that allow for 0 values, but these are not available in GENMOD.
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