MLEpoisBCD: Maximum Likelihood Estimation for a Bivariate Poisson...

In BCD: Bivariate Distributions via Conditional Specification

Maximum Likelihood Estimation for a Bivariate Poisson Distribution via Conditional Specification

Description

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

Usage

MLEpoisBCD(data, initial_values = NULL)

Arguments

data	data frame or matrix with two columns, representing paired observations of count variables (X, Y).
initial_values	optional named list with initial values for the parameters: lambda1, lambda2, and lambda3. If not provided, the function computes heuristic starting values.

Details

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

P(X = x, Y = y) = K(\lambda_1, \lambda_2, \lambda_3) \frac{\lambda_1^x \lambda_2^y \lambda_3^{xy}}{x! y!},

where x, y = 0, 1, 2, \ldots , and K(\lambda_1, \lambda_2, \lambda_3) is the normalizing constant.

Value

A list of class "MLEpoisBCD" containing:

lambda1

estimated lambda1.

lambda2

estimated lambda2.

lambda3

estimated dependence parameter (must be in (0, 1]).

logLik

Maximum log-likelihood achieved.

AIC

Akaike Information Criterion.

BIC

Bayesian Information Criterion.

convergence

Convergence status from the optimizer (0 means successful).

See Also

dpoisBCD ppoisBCD rpoisBCD

Examples

# Simulate data
data <- rpoisBCD(n = 50, lambda1 = 3, lambda2 = 5, lambda3 = 1)
result <- MLEpoisBCD(data)
print(result)

data(eplSeasonGoals)
MLEpoisBCD(eplSeasonGoals[["1819"]])

data(lensfaults)
MLEpoisBCD(lensfaults)

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