Merge pull request #447 from spsanderson/development

Fixes #430

NAMESPACE

@@ -123,6 +123,7 @@ export(util_negative_binomial_stats_tbl)
 export(util_normal_aic)
 export(util_normal_param_estimate)
 export(util_normal_stats_tbl)
+export(util_pareto_aic)
 export(util_pareto_param_estimate)
 export(util_pareto_stats_tbl)
 export(util_poisson_param_estimate)

R/utils-aic-pareto.R

@@ -0,0 +1,78 @@
+#' Calculate Akaike Information Criterion (AIC) for Pareto Distribution
+#'
+#' This function calculates the Akaike Information Criterion (AIC) for a Pareto distribution fitted to the provided data.
+#'
+#' @family Utility
+#' @author Steven P. Sanderson II, MPH
+#'
+#' @description
+#' This function estimates the shape and scale parameters of a Pareto distribution
+#' from the provided data using maximum likelihood estimation,
+#' and then calculates the AIC value based on the fitted distribution.
+#'
+#' @param .x A numeric vector containing the data to be fitted to a Pareto distribution.
+#'
+#' @details
+#' This function fits a Pareto distribution to the provided data using maximum
+#' likelihood estimation. It estimates the shape and scale parameters
+#' of the Pareto distribution using maximum likelihood estimation. Then, it
+#' calculates the AIC value based on the fitted distribution.
+#'
+#' Initial parameter estimates: The function uses the method of moments estimates
+#' as starting points for the shape and scale parameters of the Pareto distribution.
+#'
+#' Optimization method: The function uses the optim function for optimization.
+#' You might explore different optimization methods within optim for potentially
+#' better performance.
+#'
+#' Goodness-of-fit: While AIC is a useful metric for model comparison, it's
+#' recommended to also assess the goodness-of-fit of the chosen model using
+#' visualization and other statistical tests.
+#'
+#' @examples
+#' # Example 1: Calculate AIC for a sample dataset
+#' set.seed(123)
+#' x <- TidyDensity::tidy_pareto()$y
+#' util_pareto_aic(x)
+#'
+#' @return
+#' The AIC value calculated based on the fitted Pareto distribution to the provided data.
+#'
+#' @name util_pareto_aic
+NULL
+
+#' @export
+#' @rdname util_pareto_aic
+util_pareto_aic <- function(.x) {
+  # Tidyeval
+  x <- as.numeric(.x)
+
+  # Negative log-likelihood function for Pareto distribution
+  neg_log_lik_pareto <- function(par, data) {
+    shape <- par[1]
+    scale <- par[2]
+    n <- length(data)
+    -sum(actuar::dpareto(data, shape = shape, scale = scale, log = TRUE))
+  }
+
+  # Get initial parameter estimates: method of moments
+  pe <- TidyDensity::util_pareto_param_estimate(x)$parameter_tbl |>
+    subset(method == "MLE")
+
+  # Fit Pareto distribution using optim
+  fit_pareto <- optim(
+    c(pe$shape, pe$scale),
+    neg_log_lik_pareto,
+    data = x
+  )
+
+  # Extract log-likelihood and number of parameters
+  logLik_pareto <- -fit_pareto$value
+  k_pareto <- 2 # Number of parameters for Pareto distribution (shape and scale)
+
+  # Calculate AIC
+  AIC_pareto <- 2 * k_pareto - 2 * logLik_pareto
+
+  # Return AIC
+  return(AIC_pareto)
+}