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# Getting Started

## A • STATISTICAL

A • STATISTICAL DISTRIBUTIONS Exponential(): EXPONENTIAL(Mean) or EXPO(Mean) Probability Density Function f(x) = 1 --e – x 0 otherwise for x > 0 Parameters The mean () specified as a positive real number. Range [0, + Mean Variance 2 Applications This distribution is often used to model inter-event times in random arrival and breakdown processes, but it is generally inappropriate for modeling process delay times. In Arena’s Create module, the Schedule option automatically samples from an exponential distribution with a mean that changes according to the defined schedule. This is particularly useful in service applications, such as retail business or call centers, where the volume of customers changes throughout the day. 159

GETTING STARTED WITH ARENA Gamma(, ): GAMMA(Beta, Alpha) or GAMM(Beta, Alpha) Probability Density Function f(x) = – x – 1 e ----------------------------------- – x 0 otherwise for x > 0 Unbounded FamilyBounded Family where is the complete gamma function given by = t – 1 e – 1 dt 0 Parameters Shape parameter () and scale parameter ) specified as positive real values. Range [0, + Mean Variance 2 Applications For integer shape parameters, the gamma is the same as the Erlang distribution. The gamma is often used to represent the time required to complete some task (for example, a machining time or machine repair time). 160

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