Variance of the Occupancy Distribution

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Description

Returns the variance of the occupancy distribution based on a multinomial distribution.

Usage

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varMult(n, p, iter=NULL, seed=NULL, experimental=NULL)

Arguments

n

number of attempts in the multinomial distribution

p

probabilities for landing in a specific bin

iter

number of iterations used in the Monte-Carlo approximation

seed

seed for the random number generator

experimental

access to other functions of multinomials

Details

This functions computes the variance of the occupancy distribution for a multinomial. In other words, the expected number of bins with at least one ball. The experimental argument "oneBall" computes variance of bins with exactly one ball and the experimental argument "nextTo" computes the variance of bins with one ball next to a bin with zero balls. Consider any functionality through the experimental argument untested.

Value

Returns a numeric

Author(s)

Oliver Will owill4@yahoo.com

References

See the book chapter O. Will (**) in ** for specific details about this package or Johnson, N. L. and Kotz, S. (1977) Urn Models and Their Application: An Approach to Modern Discrete Probability Theory. John Wiley & Sons, New York, NY.

Examples

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n <- 20
p <- c(seq(10,1,-1),47)/100
p <- p/sum(p)
varMult(n,p)
varMult(n,p,iter=1000,seed=4)