BCD (version 0.1.1)

pbinomBCD: 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)

Value

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

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.

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. 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)