It is very frequently used in statistics. First of all, multiplying a Chi-square random variable by a constant you obtain a Gamma random variable. So, for example, most estimates of variance obtained in inferential statistics have a Gamma distribution. The Gamma distribution can also be obtained by summing exponential random variables. So, the Gamma distribution pops out in models where the exponential distribution is used (e.g. reliability, credit risk). It is also used for Internet traffic modeling.

See the StatLect entry (link below) for an introduction.

There is abig difference between them..gamma is a distribution but central limit theorm is just like a method or technique u use to approximate gamma to another distriution which is normal....stupid

According to the links, Karl Pearson was first to formally introduce the gamma distribution. However, the symbol gamma for the gamma function, as a part of calculus, originated far earlier, by Legrenge (1752 to 1853). The beta and gamma functions are related. Please review the related links, particularly the second one from Wikipedia.

It can be thought of as a generalization of the Chi-square distribution. See the link to a related WikiAnswer question below.