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Statistics[Distributions]

  

Uniform

  

uniform (rectangular) distribution

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

Uniform(a, b)

UniformDistribution(a, b)

Parameters

a

-

lower bound parameter

b

-

upper bound parameter

Description

• 

The uniform distribution is a continuous probability distribution with probability density function given by:

ft&equals;piecewiset<a&comma;0&comma;t<b&comma;1ba&comma;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.

Examples

withStatistics&colon;

XRandomVariableUniforma&comma;b&colon;

PDFX&comma;u

&lcub;0u<a1bau<b0otherwise

(1)

PDFX&comma;0.5

&lcub;0.0.5<a1b1.a0.5<b0.otherwise

(2)

MeanX

12a&plus;12b

(3)

VarianceX

112ba2

(4)

References

  

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]

Statistics[Distributions][DiscreteUniform]

Statistics[RandomVariable]

 


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