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Statistics[Distributions]

  

Geometric

  

geometric distribution

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

Geometric(p)

GeometricDistribution(p)

Parameters

p

-

probability of success

Description

• 

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

ft&equals;piecewiset<0&comma;0&comma;p1pt

  

subject to the following conditions:

0<p&comma;p1

• 

The geometric distribution has the lack of memory property: the probability of an event occurring in the next time interval of an exponential distribution is independent of the amount of time that has already passed.

• 

The geometric variate is a special case of the NegativeBinomial variate with number of trials parameter x&equals;1.

• 

The continuous analog of the geometric variate is the Exponential variate.

• 

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

Examples

withStatistics&colon;

XRandomVariableGeometricp&colon;

ProbabilityFunctionX&comma;u

&lcub;0u<0p1puotherwise

(1)

ProbabilityFunctionX&comma;2

p1p2

(2)

MeanX

1pp

(3)

VarianceX

1pp2

(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[RandomVariable]

 


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