pbivpois {bivpois}R Documentation

Probability Function of the 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=NULL, lambda = c(1, 1, 1), log = FALSE)

Arguments

x Matrix or Vector containing the data. If x is a matrix then we consider as $x$ the first column and $y$ the second column. Additional columns and y are ignored.
y Vector containing the data of $y$. It is used only if x is also a vector. Vectors x and y should be of equal length.
lambda Vector (of length 3) containing values of the parameters $λ_1$, $λ_2$ and $λ_3$ of the bivariate Poisson distribution.
log Logical argument for calculating the log probability or the probability function. The default value is FALSE.

Details

This function evaluates the probability function (or the log) of the bivariate Poisson distribution with parameters $λ_1$, $λ_2$ and $λ_3$. Much faster than bivpois.table since it avoid `for-loops' and does not use recursive relations.

Value

A vector of values of the probabilities of $PD(λ_1, λ_2, λ_3)$ evaluated at $(x,y)$ when log=FALSE or the log-probabilities of $PD(λ_1, λ_2, λ_3)$ evaluated at $(x,y)$ when log=TRUE.

Author(s)

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

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

References

1. Karlis, D. and Ntzoufras, I. (2005). Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in R. Journal of Statistical Software (to appear).

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.

See Also

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

Examples


# probability function of (x,y)=(3,1) for lambda_1=1, lambda_2=1, lambda_3=1
pbivpois(3, 1)                              
# probability function of (x,y)=(3,1) for lambda_1=3, lambda_2=1, lambda_3=1
pbivpois(3, 1, lambda=c(3,1,1))             
# log-probability function of (x,y)=(3,1) for lambda_1=1, lambda_2=1, lambda_3=1
pbivpois(3, 1, lambda=c(3,1,1), log=TRUE)   
#
# evaluates f(1,1), f(1,3) and f(3,1) for PD(2,1,0.2)
pbivpois( c(1,3,1), c(1,1,3), c( 2,1,0.2 ) )               
# same as above
pbivpois( cbind(c(1,3,1), c(1,1,3)), lambda=c( 2,1,0.2 ) ) 


[Package bivpois version 0.50-3 Index]