Approximate Convolution of the Gamma and Mixed Gamma Distributions

The unmixed gamma distribution has been used extensively in fitting precipitation data. After the author [l] proposed a mixed distribution for precipitation series where zeros occur this distribution also began to be widely employed. Since it is often necessary to add precipitation, i.e. June plus July, for example, it is a great convenience to be able to accomplish this analytically and so avoid tabulating and fitting the summed series. The approximate convolution of two unmixed precipitation distributions was first given in [2]. Since then the approximation has been tested many times and extended to the sum of any number of variates. More recently, an approximate convolution of the mixed gamma distribution has been developed. Both approximations are discussed here.