MLEgeomBCD: Maximum Likelihood Estimation for a Bivariate Geometric...

In BCD: Bivariate Distributions via Conditional Specification

Maximum Likelihood Estimation for a Bivariate Geometric Distribution via Conditional Specification

Description

Estimates the parameters of a bivariate geometric distribution via Conditional Specification using maximum likelihood.

Usage

MLEgeomBCD(data, initial_values = c(0.5, 0.5, 0.5))

Arguments

data	data frame or matrix with two columns, representing paired observations of count variables (X, Y).
initial_values	numeric vector of length 3 with initial values for the parameters q1, q2, and q3. Must be strictly between 0 and 1. Default is c(0.5, 0.5, 0.5).

Details

The model estimates parameters from a joint distribution for (X, Y) with the form:

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.

Value

A list containing:

q1

estimated q1.

q2

estimated q2.

q3

estimated q3.

logLik

Maximum log-likelihood achieved.

AIC

Akaike Information Criterion.

BIC

Bayesian Information Criterion.

convergence

Convergence status from the optimizer (0 means successful).

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, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/03610918.2021.2004419")}

See Also

dgeomBCD pgeomBCD rgeomBCD

Examples

# Simulate data
samples <- rgeomBCD(n = 50, q1 = 0.2, q2 = 0.2, q3 = 0.5)
result <-MLEgeomBCD(samples)
print(result)
# For better estimation accuracy and stability, consider increasing the sample size (n = 1000)

data(abortflights)
MLEgeomBCD(abortflights)

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