In this paper, we assume [W.sub.i] to be a Gamma random variable whose mean and variance are given by the following :
Moschopoulos, "The distribution of the sum of independent gamma random variables," Annals of the Institute of Statistical Mathematics, vol.
Therefore, the distribution of the mean of random sample from Weibull distribution is not easy to compute whereas the distribution of sum of independent and identically distributed (i.i.d) gamma random variables
is well known.
Expressions for the PDF and the CDF of the summation of L independent Gamma random variables
were initially derived by Mathai in .
Jorgensen and Souza (1994) suggested a Poisson sum of Gamma random variables
called Tweedie to estimate insurance risk.
We are also presently examining an application of the growth method for estimating the mean of Gamma random variables