FITTING SIMULATED RUN LENGTH DISTRIBUTION USING TRANSLATED GAMMA DISTRIBUTION - Fok Seng, Chong; Ah Hin, Pooi (Malaysian Journal of Science, 2004)
Theoretically iterative formulas can be used to find the run length distribution of the two-sided CUSUM scheme. But in practice, we face the problem of requiring long computing time to get the run length distribution using the iterative formulas. An alternative way of finding the run length distribution is by means of simulation. As the simulated run length distribution exhibits random fluctuation when compared with the actual distribution, we can improve the simulated distribution by fitting it with a smooth curve. It is found that the curve given by the right tail of the translated gamma distribution gives a good fit to the simulated results. The methods based on moments and least squares are used to estimate the parameters of the translated gamma distribution. Numerical examples in the case when the observations have an exponential or normal distribution are presented.