dbinomBCD {BCD} | R Documentation |
Joint Probability Mass Function for a Bivariate Binomial Distribution via Conditional Specification
Description
Computes the probability mass function (p.m.f.) of the bivariate binomial conditionals distribution (BBCD) as defined by Ghosh, Marques, and Chakraborty (2025). The distribution is characterized by conditional binomial distributions for X
and Y
.
Usage
dbinomBCD(x, y, n1, n2, p1, p2, lambda)
Arguments
x |
value of |
y |
value of |
n1 |
number of trials for |
n2 |
number of trials for |
p1 |
base success probability for |
p2 |
base success probability for |
lambda |
dependence parameter, must be positive. |
Details
The joint p.m.f. of the BBCD is
P(X = x, Y = y) = K_B(n_1, n_2, p_1, p_2, \lambda) \binom{n_1}{x} \binom{n_2}{y} p_1^x p_2^y (1 - p_1)^{n_1 - x} (1 - p_2)^{n_2 - y} \lambda^{xy},
where x = 0, 1, \ldots, n_1
, y = 0, 1, \ldots, n_2
, and K_B(n_1, n_2, p_1, p_2, \lambda)
is the normalizing constant.
Value
The probability P(X = x, Y = y)
.
References
Ghosh, I., Marques, F., & Chakraborty, S. (2025). A form of bivariate binomial conditionals distributions. Communications in Statistics - Theory and Methods, 54(2), 534–553. doi:10.1080/03610926.2024.2315294
See Also
pbinomBCD
rbinomBCD
MLEbinomBCD
Examples
# Compute P(X = 2, Y = 1) with n1 = 5, n2 = 5, p1 = 0.5, p2 = 0.4, lambda = 0.5
dbinomBCD(x = 2, y = 1, n1 = 5, n2 = 5, p1 = 0.5, p2 = 0.4, lambda = 0.5)
# Example with independence (lambda = 1)
dbinomBCD(x = 2, y = 1, n1 = 5, n2 = 5, p1 = 0.5, p2 = 0.4, lambda = 1.0)