BCD (version 0.1.1)

MLEgeomBCD: 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))

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).

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.

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, 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)