5. Gamma

Karl Pearson, a famous British Professor, introduced the gamma distribution in 1895. The distribution, originally called the Pearson type III distribution, was renamed in the 1930s to the gamma distribution. The gamma distribution has many shapes ranging from an exponential-like to a normal-like. The distribution has two parameters, k and θ, where both are larger than zero. When k is a positive integer, the distribution is the same as the Erlang. Also, when k is less or equal to one, the mode is zero and the distribution is exponential-like; and when k is larger than one, the mode is greater than zero. As k increases, the shape is like a normal distribution. There is no closed form solution to compute the cumulative probability, but quantitative methods have been developed and are available. Another method is developed in this chapter and applies when k ranges from 1 to 9. When sample data is available, estimates of the parameter values are obtained. When no sample data is available, estimates of the parameter values are obtained using approximations on some distribution measures.