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Statistics[Distributions]

  

DiscreteUniform

  

discrete uniform distribution

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

DiscreteUniform(a, b)

DiscreteUniformDistribution(a, b)

Parameters

a

-

lower bound parameter

b

-

upper bound parameter

Description

• 

The discrete uniform distribution is a discrete probability distribution with probability function given by:

ft=0t<a1ba+1tb0otherwise

  

subject to the following conditions:

ab

• 

Note that the DiscreteUniform command is inert and should be used in combination with the RandomVariable command.

Examples

withStatistics&colon;

XRandomVariableDiscreteUniforma&comma;b&colon;

ProbabilityFunctionX&comma;u

0u<a1ba+1ub0otherwise

(1)

ProbabilityFunctionX&comma;4

04<a1ba+14b0otherwise

(2)

MeanX

a2+b2

(3)

The variance of X is a somewhat messy expression, because of all the ceil and floor functions.

VarianceX

a212+b212+b6ab6a6

(4)

If we know that a and b are integers, we can apply these assumptions to make the expression easier to read.

VarianceXassuminga::integer&comma;b::integer

112a2+112b2+16b16ab16a

(5)

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][Uniform]

Statistics[RandomVariable]