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Math and Statistical Distributions
Probability distributions
Distribution Binomial
Cauchy
Chi Squared Constant
Empirical
Erlang Exponential
Extreme Value Type 1A
Extreme Value Type 1B
Gamma
Definition
The number of outcomes in a given number of trials. Most often used to express success/failure rates or the results of experiments, such as the num- ber of defective items in a batch or the number of customers who will arrive who are of a particular type.
Used to represent the ratio of two equally distributed parameters in certain cases or wildly divergent data as long as the data has a central tendency. It has a sharp central peak but broad tails that are much heavier than the tails of the Normal distribution.
Used in statistical tests but, since it does not have a scaling parameter, its uti- lization is somewhat limited. It is a subset of the Gamma distribution with beta = 2 and alpha = nu/2.
This does not produce a random number, but a constant value which does not change. Used when there is exactly the same amount of time between arriv- als or as a method to reduce the effects of randomness in the early stages of model building.
Used to generate a customized or user-defined distribution with a special shape when the probability of occurrence is known. The options are: dis- crete (the block will output the exact values given in the table); stepped (values in the table will be used as probabilities of ranges of data); and interpolated (the probability distribution will be interpolated between the data points).
Frequently used for queueing theory to represent service times for various activities or when modeling telephone traffic.
Primarily used to define intervals between occurrences such as the time between arrivals of customers or orders and the time between failures (TBF) or time to repair (TTR) for electrical equipment. Also used for activity times such as repair times or the duration of telephone conversations.
describes the limiting distribution of the greatest values of many types of samples. Used to represent parameters in growth models, astronomy, human lifetimes, radioactive emissions, strength of materials, flood analysis, seis- mic analysis, and rainfall analysis. Its peaked shape is always the same but it may be shifted or scaled.
Describes the limiting distribution of the least values of many types of sam- ples. Represents parameters in growth models, astronomy, human lifetimes, radioactive emissions, strength of materials, flood analysis, seismic analysis, and rainfall analysis.
Typically used to represent the time required to complete some task. The dis- tribution is shaped like a decaying exponential for shape (2) values between 0 and 1. For shape values greater than 1, the distribution is shaped like a bell curve skewed towards the low end.
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