Poisson random variable - Maple Help

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Student[Statistics][PoissonRandomVariable] - Poisson random variable

Calling Sequence

PoissonRandomVariable(lambda)

Parameters

lambda

-

intensity parameter

Description

• 

The Poisson random variable is a discrete probability random variable with probability function given by:

ft=0t<0λt&ExponentialE;λt!otherwise

  

subject to the following conditions:

0<λ

Notes

• 

The Quantile and CDF functions applied to a Poisson random variable use a sequence of iterations in order to converge upon the desired output point.  The maximum number of iterations to perform is equal to 100 by default, but this value can be changed by setting the environment variable _EnvStatisticsIterations to the desired number of iterations.

Examples

withStudent&lsqb;Statistics&rsqb;&colon;

X:=PoissonRandomVariable&lambda;&colon;

ProbabilityFunctionX&comma;u

&lcub;0u<0&lambda;u&ExponentialE;&lambda;u&excl;otherwise

(1)

ProbabilityFunctionX&comma;2

12&lambda;2&ExponentialE;&lambda;

(2)

MeanX

&lambda;

(3)

VarianceX

&lambda;

(4)

Y:=PoissonRandomVariable3&colon;

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

CumulativeDistributionFunctionY&comma;x&comma;output&equals;plot

See Also

Statistics[Distributions][Poisson], Statistics[RandomVariable], Student, Student[Statistics]

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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