pbinomBCD: Cumulative Distribution Function for a Bivariate Binomial...

In BCD: Bivariate Distributions via Conditional Specification

Cumulative Distribution Function for a Bivariate Binomial Distribution via Conditional Specification

Description

Computes the cumulative distribution function (c.d.f.) of a bivariate binomial conditionals distribution (BBCD) as defined by Ghosh, Marques, and Chakraborty (2025).

Usage

pbinomBCD(x, y, n1, n2, p1, p2, lambda)

Arguments

x	value at which the c.d.f. is evaluated
y	value at which the c.d.f. is evaluated
n1	number of trials for X , must be non-negative.
n2	number of trials for Y , must be non-negative.
p1	base success probability for X , in (0, 1).
p2	base success probability for Y , in (0, 1).
lambda	dependence parameter, must be positive.

Value

The probability P(X \leq x, Y \leq y) .

References

Ghosh, I., Marques, F., & Chakraborty, S. (2025). A form of bivariate binomial conditionals distributions. Communications in Statistics - Theory and Methodsm 54(2), 534–553. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/03610926.2024.2315294")}

See Also

dbinomBCD rbinomBCD

Examples

# Compute P(X \le 2, Y \le 1) with n1 = 5, n2 = 5, p1 = 0.5, p2 = 0.4, lambda = 0.5
pbinomBCD(x = 2, y = 5, n1 = 5, n2 = 5, p1 = 0.5, p2 = 0.4, lambda = 0.5)

# Example with independence (lambda = 1)
pbinomBCD(x = 1, y = 1, n1 = 10, n2 = 10, p1 = 0.3, p2 = 0.6, lambda = 1)

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