Merge pull request #442 from spsanderson/development

Fixes #425

NAMESPACE

@@ -95,6 +95,7 @@ export(util_binomial_param_estimate)
 export(util_binomial_stats_tbl)
 export(util_burr_param_estimate)
 export(util_burr_stats_tbl)
+export(util_cauchy_aic)
 export(util_cauchy_param_estimate)
 export(util_cauchy_stats_tbl)
 export(util_chisq_aic)

R/utils-aic-cauchy.R

@@ -0,0 +1,83 @@
+#' Calculate Akaike Information Criterion (AIC) for Cauchy Distribution
+#'
+#' This function calculates the Akaike Information Criterion (AIC) for a Cauchy
+#' distribution fitted to the provided data.
+#'
+#' @family Utility
+#' @author Steven P. Sanderson II, MPH
+#'
+#' @description
+#' This function estimates the parameters of a Cauchy 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 Cauchy
+#' distribution.
+#'
+#' @details
+#' This function fits a Cauchy distribution to the provided data using maximum
+#' likelihood estimation. It first estimates the initial parameters of the
+#' Cauchy distribution using the method of moments. Then, it optimizes the
+#' negative log-likelihood function using the provided data and the initial
+#' parameter estimates. Finally, it calculates the AIC value based on the
+#' fitted distribution.
+#'
+#' Initial parameter estimates: The function uses the method of moments estimates
+#' for the initial location and scale parameters of the Cauchy 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 <- rcauchy(30)
+#' util_cauchy_aic(x)
+#'
+#' @return
+#' The AIC value calculated based on the fitted Cauchy distribution to the
+#' provided data.
+#'
+#' @name util_cauchy_aic
+NULL
+
+#' @export
+#' @rdname util_cauchy_aic
+util_cauchy_aic <- function(.x) {
+  # Tidyeval
+  x <- as.numeric(.x)
+
+  # Negative log-likelihood function for Cauchy distribution
+  neg_log_lik_cauchy <- function(par, data) {
+    location <- par[1]
+    scale <- par[2]
+    n <- length(data)
+    -sum(dcauchy(data, location = location, scale = scale, log = TRUE))
+  }
+
+  # Get initial parameter estimates (you might need to adjust this depending on your data)
+  # Here we use method of moments estimates as a starting point
+  pe <- TidyDensity::util_cauchy_param_estimate(x)$parameter_tbl
+
+  # Fit Cauchy distribution using optim
+  fit_cauchy <- optim(
+    c(pe$location, pe$scale),
+    neg_log_lik_cauchy,
+    data = x
+  )
+
+  # Extract log-likelihood and number of parameters
+  logLik_cauchy <- -fit_cauchy$value
+  k_cauchy <- 2 # Number of parameters for Cauchy distribution (location and scale)
+
+  # Calculate AIC
+  AIC_cauchy <- 2 * k_cauchy - 2 * logLik_cauchy
+
+  # Return AIC
+  return(AIC_cauchy)
+}