Statistics/Distributions/Uniform

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Continuous Uniform Distribution[edit]

Uniform
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.
Notation
Parameters
Support
PDF
CDF
Mean
Median
Mode any value in
Variance
Skewness 0
Ex. kurtosis
Entropy
MGF
CF

The (continuous) uniform distribution, as its name suggests, is a distribution with probability densities that are the same at each point in an interval. In casual terms, the uniform distribution shapes like a rectangle.

Mathematically speaking, the probability density function of the uniform distribution is defined as

And the cumulative distribution function is:

Mean[edit]

We derive the mean as follows.

As the uniform distribution is 0 everywhere but [a, b] we can restrict ourselves that interval

Variance[edit]

We use the following formula for the variance.

External links[edit]