Proses Poisson Majemuk

The Poisson process is a counting process {N(t); t � 0} that states the number of occurrences at specific time. In compound Poisson process, the Poisson process is a time-related set of independent, identically distributed random variables. The sum of random variables is used to establish the com- pound Poisson process. In this research, the compound Poisson process is explained by first de- termining its assumptions, variables, and parameters. Besides give the expla- nation of the compound Poisson process, also explain the properties of compo- und Poisson process such as it has stationary independent increments, variance, expectation, moment generating function, and probability generating function. Finally, there will discuss an example of compound Poisson process in a case. Based on the definition, the compound Poisson process can be expres- sed as S(t) = ΣN(t) k=1 Yk, t � 0 with Yk are independent, identically distributed random variables for k = 0, 1, ..., n. The stationary independent increments of compound Poisson process for the general case has proved in this research. The expectation and the variance of the compound Poisson process are given as follows μE[N(t)] and σ2E[N(t)] + μ2V ar(N(t)) sequentially. The moment generating function of S(t) is MS(t) = eλt(MY1 −1), and MY1 is a moment genera- ting function of Yk random variables. Furthermore, the probability generating function of S(t) similar with the probability generating function of negative binomial random variable for Yk has logarithmic distribution