dgeomBCD {BCD} | R Documentation |
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 |
y |
value of |
q1 |
probability parameter for |
q2 |
probability parameter for |
q3 |
dependence parameter, in |
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, doi:10.1080/03610918.2021.2004419
See Also
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)