Calculate log-likelihood for Gamma-distributed data

Computes the total log-likelihood for continuous positive data under the Gamma distribution. The shape parameter is estimated via the method of moments. Each observation can be weighted.

Usage

calc_log_likelihood_gamma(observed, estimated, weights = NULL, verbose = TRUE)

Arguments

observed

Numeric vector of observed positive values.

estimated

Numeric vector of expected means from the model (same length as observed).

weights

Optional numeric vector of non-negative weights, same length as observed. Default is NULL, which sets all weights to 1.

verbose

Logical; if TRUE, prints estimated shape parameter and total log-likelihood.

Value

A scalar representing the total log-likelihood (numeric).

Details

Weighted log-likelihood is summed over each observation. The shape \(\\alpha\) is estimated via method of moments from observed.

Examples

calc_log_likelihood_gamma(c(2.5, 3.2, 1.8), c(2.4, 3.0, 2.0))
#> Gamma shape (α) = 12.76
#> Gamma log-likelihood: -1.73
#> [1] -1.731035