negative binomial (Pascal) distribution - Maple Help

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Statistics[Distributions][NegativeBinomial] - negative binomial (Pascal) distribution

Calling Sequence

NegativeBinomial(x, p)

NegativeBinomialDistribution(x, p)

Parameters

x

-

number of trials

p

-

probability of success

Description

• 

The negative binomial distribution is a discrete probability distribution with probability function given by:

ft=0t<0Γx+tpx1ptΓxt!otherwise

  

subject to the following conditions:

0<x&comma;0<p&comma;p1

• 

The negative binomial distribution is also known as the Pascal distribution.

• 

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

Examples

withStatistics&colon;

X:=RandomVariableNegativeBinomialx&comma;p&colon;

ProbabilityFunctionX&comma;u

&lcub;0u<0&Gamma;x&plus;upx1pu&Gamma;xu&excl;otherwise

(1)

ProbabilityFunctionX&comma;2

12&Gamma;x&plus;2px1p2&Gamma;x

(2)

MeanX

x1pp

(3)

VarianceX

x1pp2

(4)

See Also

Statistics, Statistics[Distributions], Statistics[RandomVariable]

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.


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