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# Getting Started

## A • STATISTICAL

A • STATISTICAL DISTRIBUTIONS Applications The discrete empirical distribution is often used to incorporate discrete empirical data directly into the model. This distribution is frequently used for discrete assignments such as the job type, the visitation sequence, or the batch size for an arriving entity. 157

GETTING STARTED WITH ARENA Erlang(, k): ERLANG(ExpMean, k) or ERLA(ExpMean, k) Probability Density Function f(x) = – k x k – 1 e – x --------------------------------- k – 1! for x > 0 0 otherwise Parameters If X1, X2, . . . , Xk are independent, identically distributed exponential random variables, then the sum of these k samples has an Erlang-k distribution. The mean () of each of the component exponential distributions and the number of exponential random variables (k) are the parameters of the distribution. The exponential mean is specified as a positive real number, and k is specified as a positive integer. Range [0, + Mean k Variance k 2 Applications The Erlang distribution is used in situations in which an activity occurs in successive phases and each phase has an exponential distribution. For large k, the Erlang approaches the normal distribution. The Erlang distribution is often used to represent the time required to complete a task. The Erlang distribution is a special case of the gamma distribution in which the shape parameter, , is an integer (k). 158

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