dpoisBCD: Joint Probability Mass Function for a Bivariate Poisson...

View source: R/dpoisBCD.R

dpoisBCDR Documentation

Joint Probability Mass Function for a Bivariate Poisson Distribution via Conditional Specification

Description

Computes the joint probability mass function (p.m.f.) of a Bivariate Poisson Conditionals distribution (BPCD) based on Ghosh, Marques, and Chakraborty (2021).

Usage

dpoisBCD(x, y, lambda1, lambda2, lambda3)

Arguments

x

value of X that must be a non-negative integer

y

value of Y that must be a non-negative integer

lambda1

rate parameter for X that must be positive

lambda2

rate parameter for Y that must be positive

lambda3

dependence parameter that must be (0, 1]

Details

The joint p.m.f. of the BGCD is

P(X = x, Y = y) = K(\lambda_1, \lambda_2, \lambda_3) \frac{\lambda_1^x \lambda_2^y \lambda_3^{xy}}{x! y!},

where x, y = 0, 1, 2, \ldots , and K(\lambda_1, \lambda_2, \lambda_3) is the normalizing constant computed by the function normalize_constant_BPCD.

Key properties of the BPCD include:

- Negative correlation for \lambda_3 < 1 ,

- Independence for \lambda_3 = 1 .

Value

probability P(X = x, Y = y) for each pair of x and y .

References

Ghosh, I., Marques, F., & Chakraborty, S. (2021). A new bivariate Poisson distribution via conditional specification: properties and applications. Journal of Applied Statistics, 48(16), 3025-3047. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/02664763.2020.1793307")}

See Also

rpoisBCD, ppoisBCD

Examples

# Compute P(X = 1, Y = 2) with lambda1 = 0.5, lambda2 = 0.5, lambda3 = 0.5
dpoisBCD(x = 1, y = 2, lambda1 = 0.5, lambda2 =  0.5, lambda3 =  0.5)

# Compute P(X = 0, Y = 1) with lambda1 = 0.5, lambda2 = 0.5, lambda3 = 0.5
dpoisBCD(x = 0, y = 1, lambda1 = 0.5, lambda2 =  0.5, lambda3 =  0.5)


BCD documentation built on June 25, 2025, 5:09 p.m.