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Continuous uniform distribution

Uniform distribution on an interval / From Wikipedia, the free encyclopedia

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In probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds.[1] The bounds are defined by the parameters, and which are the minimum and maximum values. The interval can either be closed (i.e. ) or open (i.e. ).[2] Therefore, the distribution is often abbreviated where stands for uniform distribution.[1] The difference between the bounds defines the interval length; all intervals of the same length on the distribution's support are equally probable. It is the maximum entropy probability distribution for a random variable under no constraint other than that it is contained in the distribution's support.[3]

Quick facts: Notation, Parameters, Support, PDF, CDF...
Probability density function
PDF of the uniform probability distribution using the maximum convention at the transition points.
Using maximum convention
Cumulative distribution function
CDF of the uniform probability distribution.
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