Gamma Random Variables

        A random variable is called a gamma random variable with parameters if its PDF is given by       

    where is the gamma function. are called shape and scale parameters respectively.

• The gamma distribution can assume different shapes for different values of as shown in Figure 7 and Figure 8. For , is a strictly decreasing function of asymptotically approaching 0 as .. For , has a unique mode at the location
                                      

              and of value

• The gamma distribution is important because many practical data can be fitted with it.