BCD (version 0.1.1)

dgeomBCD: 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)

Value

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

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 \(Y\)

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, 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)