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Math and Statistical Distributions
Probability distributions
Distribution Normal
Pareto
Pearson Type V Pearson Type VI Poisson
Power Function Rayleigh Triangular
Uniform Integer Uniform Real Weibull
Definition
The well-known Gaussian or bell curve. Most often used when events are due to natural rather than man-made causes, to represent quantities that are the sum of a large number of other quantities, or to represent the distribution of errors.
Represents the income distribution of a society. It is also used to model many empirical phenomena with very long right tails, such as city popula- tion sizes, occurrence of natural resources, stock price fluctuations, size of firms, brightness of comets, and error clustering in communication circuits.
A distribution typically used to represent the time required to complete some task. The density takes on shapes similar to lognormal, but can have a larger “spike” close to x = 0.
A distribution typically used to represent the time required to complete some task. A continuous distribution bounded by zero on the left and unbounded on the right.
Models the rate of occurrence, such as the number of telephone calls per minute, the number of errors per page, or the number of arrivals to the sys- tem within a given time period. Note that in queueing theory, arrival rates are often specified as poisson arrivals per time unit. This corresponds to an exponential interarrival time.
A continuous distribution with both upper and lower finite bounds. It is a special case of the Beta distribution with q = 1. The Uniform distribution is a special case of the Power Function distribution with p = 1.
Frequently used to represent lifetimes because its hazard rate increases lin- early with time, e.g. the lifetime of vacuum tubes. This distribution also finds application in noise problems in communications.
Usually more appropriate for business processes than the uniform distribu- tion since it provides a good first approximation of the true values. Used for activity times where only three pieces of information (the minimum, the maximum, and the most likely values) are known.
Describes a integer value that is likely to fall anywhere within a specified range. Used to represent the duration of an activity if there is minimal infor- mation known about the task.
Describes a real value that is likely to fall anywhere within a specified range. Used to represent the duration of an activity if there is minimal information known about the task.
Commonly used to represent product life cycles and reliability issues for items that wear out, such as the time between failures (TBF) or time to repair (TTR) for mechanical equipment.
These distributions and their arguments are described more fully in the Help of blocks that use them.
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