pbivpois{bivpois}

R Documentation

Probability function of Bivariate Poisson Distribution

Description

Returns the probability the probability (or the log) of the bivariate poisson distribution for values x and y.

Usage

pbivpois(x, y, lambda = c(1, 1, 1), log=FALSE)

Required Arguments

x, y

single values containing which values should evaluated

Optional Arguments

lambda

Vector (of length 3) containing values of the parameters ë1, ë2 and ë3 of the bivariate poisson distribution.

log

Logical argument for calculating the log probability or the probability function. The default value is false (calculates the probability function)

Details

This function evaluates the probability function (or the log) of the bivariate Poisson distribution with parameters ë1, ë2 and ë3. Much faster than bivpois.table since it avoid `for-loops' and does not use recursive relations.

Value

A single value of the probability of PD(ë1, ë2 , ë3.) evaluated at (x,y) when log=TRUE or the log-probability of PD(ë1, ë2 , ë3.) evaluated at (x,y) when log=FALSE

References

1.      Karlis, D. and Ntzoufras, I. (2004). Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in S. (submitted). Technical Report, Department of Statistics, Athens University of Economics and Business, Athens, Greece.

2.      Karlis, D. and Ntzoufras, I. (2003). Analysis of Sports Data Using Bivariate Poisson Models. Journal of the Royal Statistical Society, D, (Statistician), 52, 381 – 393.

Authors Information

1.      Dimitris Karlis, Department of Statistics, Athens University of Economics and Business, Athens, Greece, e-mail: karlis@aueb.gr .

2.      Ioannis Ntzoufras, Department of Statistics, Athens University of Economics and Business, Athens, Greece, e-mail: ntzoufras@aueb.gr  .

See Also

bivpois.table,  simple.bp, lm.bp, lm.dibp .

Examples

pbivpois(3, 1)                        # probability function of (x,y)=(3,1) for ë1=1, ë2=1, ë3=1

pbivpois(3, 1, lambda=(3,1,1))        # probability function of (x,y)=(3,1) for ë1=3, ë2=1, ë3=1

pbivpois(3, 1, lambda=(3,1,1), log=T) # log-probability function of (x,y)=(3,1) for ë1=3,ë2=1, ë3=1

 


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