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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=0t<0p1ptotherwise

  

subject to the following conditions:

0<p,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=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.

• 

Note that the distribution above is for the number of failures before the first success. The other common convention is for the number of trials with the last being the first success. That is, the other convention would have p1pt1 in the probability function.

Examples

withStatistics&colon;

XRandomVariableGeometricp&colon;

ProbabilityFunctionX&comma;u

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]