dgeomBCD: Joint Probability Mass Function for A Bivariate Geometric...

In BCD: Bivariate Distributions via Conditional Specification

Joint Probability Mass Function for A Bivariate Geometric Distribution via Conditional Specification

Description

Computes the joint probability mass function (p.m.f.) of a Bivariate Geometric Conditional Distributions (BGCD) based on Ghosh, Marques, and Chakraborty (2023). This distribution models paired count data with geometric conditionals, incorporating dependence between variables X and Y .

Usage

dgeomBCD(x, y, q1, q2, q3)

Arguments

x	value of X that must be non-negative integer
y	value of Y that must be non-negative integer
q1	probability parameter for X , in (0, 1]
q2	probability parameter for Y , in (0, 1]
q3	dependence parameter, in (0, 1]

Details

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

P(X = x, Y = y) = K(q_1, q_2, q_3) q_1^x q_2^y q_3^{xy},

where K(q_1, q_2, q_3) is the normalizing constant computed by the function normalize_constant_BGCD.

Note that:

- q_3 < 1 : indicates the negative correlation between X and Y

- q_3 = 1 : indicates the independence between X and Y

Value

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

References

Ghosh, I., Marques, F., & Chakraborty, S.(2023) A bivariate geometric distribution via conditional specification: properties and applications, Communications in Statistics - Simulation and Computation, 52:12, 5925–5945, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/03610918.2021.2004419")}

See Also

pgeomBCD rgeomBCD MLEgeomBCD

Examples

# Compute P(X = 1, Y = 2) with q1 = 0.5, q2 = 0.6, q3 = 0.8
dgeomBCD(x = 1, y = 2, q1 = 0.5, q2 = 0.6, q3 = 0.8)

# # Compute P(X = 0, Y = 4) with q1 = 0.5, q2 = 0.6, q3 = 0.8
dgeomBCD(x = 0, y = 4, q1 = 0.5, q2 = 0.6, q3 = 0.8)

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