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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.
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About the history of gamma distribution?
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.
What was the motivation for introducing the Gamma distribution?
It can be thought of as a generalization of the Chi-square distribution. See the link to a related WikiAnswer question below.
Why is it necessary to use a continuity correction when using a normal distribution to approximate a binomial distribution?
It is necessary to use a continuity correction when using a normal distribution to approximate a binomial distribution because the normal distribution contains real observations, while the binomial distribution contains integer observations.
What is lambda in statistics?
Lamdba (like most Greek letters in statistics) usually denotes a parameter of a distribution (usually of Poisson, gamma or exponential distributions). This will specify the entire distribution and allow for numerical analysis of the probability generating, moment generating, probability density/mass, distribution and/or cumulant functions (along with all moments), as and where these are defined.
The most commonly used greek letters in statistics?
I'll give you some common Greek symbols used in statistical analyses. I can't tell you which is the most common one given the enormous task of reviewing every statistics book. The Greek mu for mean, sigma for variance and rho for correlation are probably the first ones that one encounters in statistical analyses. Also, beta for beta distribution, gamma for gamma distribution, chi for chi-squared distribution. Alpha and beta are common as distribution parameters. In derivations, delta is common for differences of variables. Tau is common for a time variable. You will find more information in the related link.
