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``````Math and Statistical Distributions 705
Probability distributions
Distributions represent the data observed in real-world situations. When you gather data for a simulation model, it is seldom in a useful form. By “filling in the gaps,” distributions help to compensate for information which was overlooked during data collection. For example, distri- butions account for extreme or outlying values which may have been missed during typically short data-gathering intervals. Stochastic models use distributions as a handy method for con- verting data into useful form and inputting it into models.
Characteristics of distributions
The functions that produce a distribution have one or more parameter arguments which define and control its characteristics. The most important characteristics are a distribution’s shape, its spread, and its location or central tendency. Shape is often used to identify distributions; for example, the bell-shaped curve of a normal distribution is widely recognized. Shape can be characterized according to skewness (leaning to one side or another) and kurtosis (whether it is peaked or flat). You specify the characteristics for the selected distribution by the values you enter for these arguments.
Choosing a distribution
Using random numbers means either choosing the theoretical distribution that best describes the variability of the raw data, describing the data using a user-defined or empirical distribu- tion (such as the empirical distribution in the Create block), or fitting known data to a distribu- tion. As seen below, there are many distributions in ExtendSim and it also has the ability to interface with external distribution-fitting software, as discussed in the next topic.
The choice of one distribution over another is not an exact science, but rather is dependent on the type and extent of the data which is gathered, the detail required for the process being mod- eled, and (in the case where little data is available), informed guesswork. If the data does not fit any of the distributions described below as “typical” for your process, but fits a distribution which is not typical, go with what your data tells you. It is usually better to use an approximate distribution than it is to keep a value constant.
Distribution fitting
There are also software applications which fit data to distributions. Use these tools in situations where there is empirical data you want to model using random distributions, but the Extend- Sim distributions do not exactly fit. These products can help find the statistical distribution that best emulates the real-world data.
Some ExtendSim packages come with the Stat::Fit distribution fitting application (see “Stat::Fit (Windows only)” on page 679.) The Random Number block has a Distribution Fit- ting tab from which to launch a distribution fitting package, analyze empirical data, and deter- mine the appropriate statistical distribution for a given data set.
ExtendSim distributions
When there is sparse or no data, this guide of common uses may help you select a plausible distribution in the Create, Shutdown, or Random Number blocks, within the Sensitivity Setup dialog, or when formatting a cell in the ExtendSim database:
Distribution Definition
Beta Distribution of random proportion, such as the proportion of defective items in a shipment, or time to complete a task.
How To

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