Statistics[Distributions]
Uniform
uniform (rectangular) distribution
Calling Sequence
Parameters
Description
Examples
References
Uniform(a, b)
UniformDistribution(a, b)
a
-
lower bound parameter
b
upper bound parameter
The uniform distribution is a continuous probability distribution with probability density function given by:
f⁡t=piecewise⁡t<a,0,t<b,1b−a,0
subject to the following conditions:
a<b
The uniform variate is related to the unit parameter Beta variate by Uniform(0,1) ~ Beta(1,1).
The uniform variate is related to the unit parameter Power variate by Uniform(0,1) ~ Power(1,1).
Note that the Uniform command is inert and should be used in combination with the RandomVariable command.
For the discrete uniform distribution, see DiscreteUniform.
with⁡Statistics:
X ≔ RandomVariable⁡Uniform⁡a,b:
PDF⁡X,u
{0u<a1b−au<b0otherwise
PDF⁡X,0.5
{0.0.5<a1b−1.⁢a0.5<b0.otherwise
Mean⁡X
12⁢a+12⁢b
Variance⁡X
112⁢b−a2
Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.
Johnson, Norman L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.
Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.
See Also
Statistics
Statistics[Distributions][DiscreteUniform]
Statistics[RandomVariable]
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