negative binomial (Pascal) random variable - Maple Help

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Student[Statistics][NegativeBinomialRandomVariable] - negative binomial (Pascal) random variable

Calling Sequence

NegativeBinomialRandomVariable(x, p)

Parameters

x

-

number of trials

p

-

probability of success

Description

• 

The negative binomial random variable is a discrete probability random variable 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 random variable is also known as the Pascal random variable.

Examples

withStudent&lsqb;Statistics&rsqb;&colon;

X:=NegativeBinomialRandomVariablex&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)

Y:=NegativeBinomialRandomVariable3&comma;12&colon;

ProbabilityFunctionY&comma;x&comma;output&equals;plot

CDFY&comma;x&comma;output&equals;plot

See Also

Statistics[Distributions][NegativeBinomial], Student, Student[Statistics], Student[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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