Density computation of the bivariate Poisson distribution {bivpois}

Density computation of the bivariate Poisson distribution

Description

Density computation of the bivariate Poisson distribution.

Usage

dbp(x1, x2 = NULL, lambda, logged = TRUE)

Arguments

x1

Either a numerical vector with the values of the first variable or a matrix with 2 columns containing both variables. In the latter case, x2 must be NULL.

x2

A numerical vector with the values of the second. If x1 is a matrix with 2 columns containing both variables, x2 must be NULL.

lambda

A vector with three numbers, the estimates of the \lambda_s.

logged

Should the logarithm of the density values be computed? The default value is TRUE.

Details

The density of the bivariate Poisson distribution is computed.

Value

A vector with the logged density values.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

References

Kawamura K. (1984). Direct calculation of maximum likelihood estimator for the bivariate Poisson distribution. Kodai Mathematical Journal, 7(2): 211–221.

Kocherlakota S. and Kocherlakota K. (1992). Bivariate discrete distributions. CRC Press.

Karlis D. and Ntzoufras I. (2003). Analysis of sports data by using bivariate poisson models. Journal of the Royal Statistical Society: Series D (The Statistician), 52(3): 381–393.

See Also

rbp

Examples

x <- rbp( 300, c(3, 5, 2) )
a <- bp.mle(x)
f <- dbp(x, lambda = a$lambda)
sum(f)