Poisson

[spsanderson]

Function:

#' Calculate Akaike Information Criterion (AIC) for Poisson Distribution
#'
#' This function calculates the Akaike Information Criterion (AIC) for a Poisson 
#' distribution fitted to the provided data.
#'
#' @family Utility
#' @author Steven P. Sanderson II, MPH
#'
#' @description
#' This function estimates the lambda parameter of a Poisson distribution from the 
#' provided data and then calculates the AIC value based on the fitted distribution.
#'
#' @param .x A numeric vector containing the data to be fitted to a Poisson distribution.
#'
#' @details
#' This function fits a Poisson distribution to the provided data. It estimates the 
#' lambda parameter of the Poisson distribution from the data. Then, it calculates 
#' the AIC value based on the fitted distribution.
#' 
#' Initial parameter estimates: The function uses the method of moments estimate 
#' as a starting point for the lambda parameter of the Poisson distribution.
#' 
#' Optimization method: Since the parameter is directly calculated from the data, 
#' no optimization is needed.
#' 
#' 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 <- rpois(100, lambda = 2)
#' util_poisson_aic(x)
#'
#' @return
#' The AIC value calculated based on the fitted Poisson distribution to the provided data.
#'
#' @name util_poisson_aic
NULL

#' @export
#' @rdname util_poisson_aic
util_poisson_aic <- function(.x) {
  # Tidyeval
  x <- as.numeric(.x)
  
  # Estimate lambda parameter
  lambda <- mean(x, na.rm = TRUE)
  
  # Calculate AIC
  k_poisson <- 1 # Number of parameters for Poisson distribution (lambda)
  logLik_poisson <- sum(dpois(x, lambda = lambda, log = TRUE))
  AIC_poisson <- 2 * k_poisson - 2 * logLik_poisson
  
  # Return AIC
  return(AIC_poisson)
}

Example:

> set.seed(123)
> x <- rpois(100, lambda = 2)
> util_poisson_aic(x)
[1] 341.674
> fitdist(x, "pois", start = list(lambda = mean(x)))$aic
[1] 341.674