Fixes #473

NAMESPACE

@@ -111,6 +111,9 @@ export(util_f_stats_tbl)
 export(util_gamma_aic)
 export(util_gamma_param_estimate)
 export(util_gamma_stats_tbl)
+export(util_generalized_beta_aic)
+export(util_generalized_beta_param_estimate)
+export(util_generalized_beta_stats_tbl)
 export(util_generalized_pareto_aic)
 export(util_generalized_pareto_param_estimate)
 export(util_generalized_pareto_stats_tbl)

NEWS.md

@@ -39,6 +39,9 @@ Add function `util_inverse_burr_stats_tbl()` to create a summary table of the In
 13. Fix #474 - Add function `util_generalized_pareto_param_estimate()` to estimate the parameters of the Generalized Pareto distribution.
 Add function `util_generalized_pareto_aic()` to calculate the AIC for the Generalized Pareto distribution.
 Add function `util_generalized_pareto_stats_tbl()` to create a summary table of the Generalized Pareto distribution.
+14. Fix #473 - Add function `util_generalized_beta_param_estimate()` to estimate the parameters of the Generalized Gamma distribution.
+Add function `util_generalized_beta_aic()` to calculate the AIC for the Generalized Gamma distribution.
+Add function `util_generalized_beta_stats_tbl()` to create a summary table of the Generalized Gamma distribution.
 
 ## Minor Improvements and Fixes
 1. Fix #468 - Update `util_negative_binomial_param_estimate()` to add the use of

R/est-param-gen-beta.R

@@ -0,0 +1,125 @@
+#' Estimate Generalized Beta Parameters
+#'
+#' @family Parameter Estimation
+#' @family Generalized Beta
+#'
+#' @details This function will attempt to estimate the generalized Beta shape1, shape2, shape3, and rate
+#' parameters given some vector of values.
+#'
+#' @description The function will return a list output by default, and if the parameter
+#' `.auto_gen_empirical` is set to `TRUE` then the empirical data given to the
+#' parameter `.x` will be run through the `tidy_empirical()` function and combined
+#' with the estimated generalized Beta data.
+#'
+#' @param .x The vector of data to be passed to the function.
+#' @param .auto_gen_empirical This is a boolean value of TRUE/FALSE with default
+#' set to TRUE. This will automatically create the `tidy_empirical()` output
+#' for the `.x` parameter and use the `tidy_combine_distributions()`. The user
+#' can then plot out the data using `$combined_data_tbl` from the function output.
+#'
+#' @examples
+#' library(dplyr)
+#' library(ggplot2)
+#'
+#' set.seed(123)
+#' x <- tidy_generalized_beta(100, .shape1 = 2, .shape2 = 3,
+#' .shape3 = 4, .rate = 5)[["y"]]
+#' output <- util_generalized_beta_param_estimate(x)
+#'
+#' output$parameter_tbl
+#'
+#' output$combined_data_tbl %>%
+#'   tidy_combined_autoplot()
+#'
+#' @return
+#' A tibble/list
+#'
+#' @author Steven P. Sanderson II, MPH
+#'
+#' @export
+#'
+
+util_generalized_beta_param_estimate <- function(.x, .auto_gen_empirical = TRUE) {
+
+  # Tidyeval ----
+  x_term <- as.numeric(.x)
+  n <- length(x_term)
+
+  # Checks ----
+  if (!is.vector(x_term, mode = "numeric") || is.factor(x_term)) {
+    rlang::abort(
+      message = "'.x' must be a numeric vector.",
+      use_cli_format = TRUE
+    )
+  }
+
+  if (n < 2) {
+    rlang::abort(
+      message = "'.x' must contain at least two non-missing distinct values. All values of '.x' must be positive.",
+      use_cli_format = TRUE
+    )
+  }
+
+  # Negative log-likelihood function for generalized Beta distribution
+  genbeta_lik <- function(params, data) {
+    shape1 <- params[1]
+    shape2 <- params[2]
+    shape3 <- params[3]
+    rate <- params[4]
+    -sum(actuar::dgenbeta(data, shape1 = shape1, shape2 = shape2,
+                          shape3 = shape3, rate = rate, log = TRUE))
+  }
+
+  # Initial parameter guesses
+  initial_params <- c(shape1 = 1, shape2 = 1, shape3 = 1, rate = 1)
+
+  # Optimize to minimize the negative log-likelihood
+  opt_result <- stats::optim(
+    par = initial_params,
+    fn = genbeta_lik,
+    data = x_term
+  )
+
+  shape1 <- opt_result$par[["shape1"]]
+  shape2 <- opt_result$par[["shape2"]]
+  shape3 <- opt_result$par[["shape3"]]
+  rate <- opt_result$par[["rate"]]
+
+  # Return Tibble ----
+  if (.auto_gen_empirical) {
+    te <- tidy_empirical(.x = x_term)
+    td <- tidy_generalized_beta(.n = n, .shape1 = round(shape1, 3), .shape2 = round(shape2, 3), .shape3 = round(shape3, 3), .rate = round(rate, 3))
+    combined_tbl <- tidy_combine_distributions(te, td)
+  }
+
+  ret <- dplyr::tibble(
+    dist_type = "Generalized Beta",
+    samp_size = n,
+    min = min(x_term),
+    max = max(x_term),
+    mean = mean(x_term),
+    shape1 = shape1,
+    shape2 = shape2,
+    shape3 = shape3,
+    rate = rate
+  )
+
+  # Return ----
+  attr(ret, "tibble_type") <- "parameter_estimation"
+  attr(ret, "family") <- "generalized_beta"
+  attr(ret, "x_term") <- .x
+  attr(ret, "n") <- n
+
+  if (.auto_gen_empirical) {
+    output <- list(
+      combined_data_tbl = combined_tbl,
+      parameter_tbl     = ret
+    )
+  } else {
+    output <- list(
+      parameter_tbl = ret
+    )
+  }
+
+  return(output)
+}

R/stats-gen-beta-tbl.R

@@ -0,0 +1,87 @@
+#' Distribution Statistics
+#'
+#' @family Generalized Beta
+#' @family Distribution Statistics
+#'
+#' @details This function will take in a tibble and return the statistics
+#' of the given type of `tidy_` distribution. It is required that data be
+#' passed from a `tidy_` distribution function.
+#'
+#' @description Returns distribution statistics in a tibble.
+#'
+#' @param .data The data being passed from a `tidy_` distribution function.
+#'
+#' @examples
+#' library(dplyr)
+#'
+#' set.seed(123)
+#' tidy_generalized_beta() |>
+#'   util_generalized_beta_stats_tbl() |>
+#'   glimpse()
+#'
+#' @return
+#' A tibble
+#'
+#' @author Steven P. Sanderson II, MPH
+#'
+#' @export
+#' @rdname util_generalized_beta_stats_tbl
+util_generalized_beta_stats_tbl <- function(.data) {
+
+  # Immediate check for tidy_ distribution function
+  if (!"tibble_type" %in% names(attributes(.data))) {
+    rlang::abort(
+      message = "You must pass data from the 'tidy_dist' function.",
+      use_cli_format = TRUE
+    )
+  }
+
+  if (attributes(.data)$tibble_type != "tidy_generalized_beta") {
+    rlang::abort(
+      message = "You must use 'tidy_generalized_beta()'",
+      use_cli_format = TRUE
+    )
+  }
+
+  # Data
+  data_tbl <- dplyr::as_tibble(.data)
+
+  atb <- attributes(data_tbl)
+  shape1 <- atb$.shape1
+  shape2 <- atb$.shape2
+  shape3 <- atb$.shape3
+  rate <- atb$.rate
+  scale <- 1 / rate
+
+  # Generalized Beta statistics calculation
+  stat_mean <- ifelse(shape2 > 1, shape1 / (shape2 - 1), "undefined")
+  stat_mode <- ifelse((shape1 > 1) & (shape2 > 2), (shape1 - 1) / (shape2 - 2), "undefined")
+  stat_var <- ifelse(shape2 > 2, (shape1 * shape2) / ((shape2 - 1)^2 * (shape2 - 2)), "undefined")
+  stat_sd <- ifelse(stat_var == "undefined", "undefined", sqrt(stat_var))
+  stat_skewness <- ifelse(shape2 > 3, (2 * (shape2 - 2 * shape1) * sqrt(shape2 - 2)) / ((shape2 - 3) * sqrt(shape1 * (shape1 + shape2))), "undefined")
+  stat_kurtosis <- ifelse(shape2 > 4, 3 + (6 * (shape2^3 - 2 * shape2^2 * (shape1 - 1) + shape1^2 * (shape1 + 1))) / (shape1 * (shape1 + 1) * (shape2 - 3) * (shape2 - 4)), "undefined")
+
+  # Data Tibble
+  ret <- dplyr::tibble(
+    tidy_function = atb$tibble_type,
+    function_call = atb$dist_with_params,
+    distribution = dist_type_extractor(atb$tibble_type),
+    distribution_type = atb$distribution_family_type,
+    points = atb$.n,
+    simulations = atb$.num_sims,
+    mean = stat_mean,
+    mode = stat_mode,
+    range = paste0("0 to Inf"),
+    std_dv = stat_sd,
+    coeff_var = ifelse(stat_var == "undefined", "undefined", sqrt(stat_var) / stat_mean),
+    skewness = stat_skewness,
+    kurtosis = stat_kurtosis,
+    computed_std_skew = tidy_skewness_vec(data_tbl$y),
+    computed_std_kurt = tidy_kurtosis_vec(data_tbl$y),
+    ci_lo = ci_lo(data_tbl$y),
+    ci_hi = ci_hi(data_tbl$y)
+  )
+
+  # Return
+  return(ret)
+}

R/utils-aic-gen-beta.R

@@ -0,0 +1,89 @@
+#' Calculate Akaike Information Criterion (AIC) for Generalized Beta Distribution
+#'
+#' This function calculates the Akaike Information Criterion (AIC) for a generalized Beta
+#' distribution fitted to the provided data.
+#'
+#' @family Utility
+#'
+#' @author Steven P. Sanderson II, MPH
+#'
+#' @description
+#' This function estimates the shape1, shape2, shape3, and rate parameters of a generalized Beta 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 generalized Beta distribution.
+#'
+#' @details
+#' This function fits a generalized Beta distribution to the provided data using maximum
+#' likelihood estimation. It estimates the shape1, shape2, shape3, and rate parameters
+#' of the generalized Beta distribution using maximum likelihood estimation. Then, it
+#' calculates the AIC value based on the fitted distribution.
+#'
+#' Initial parameter estimates: The function uses reasonable initial estimates
+#' for the shape1, shape2, shape3, and rate parameters of the generalized Beta 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 <- tidy_generalized_beta(100, .shape1 = 2, .shape2 = 3,
+#'                           .shape3 = 4, .rate = 5)[["y"]]
+#' util_generalized_beta_aic(x)
+#'
+#' @return
+#' The AIC value calculated based on the fitted generalized Beta distribution to
+#' the provided data.
+#'
+#' @name util_generalized_beta_aic
+NULL
+
+#' @export
+#' @rdname util_generalized_beta_aic
+util_generalized_beta_aic <- function(.x) {
+  # Tidyeval
+  x <- as.numeric(.x)
+
+  # Negative log-likelihood function for generalized Beta distribution
+  neg_log_lik_genbeta <- function(par, data) {
+    shape1 <- par[1]
+    shape2 <- par[2]
+    shape3 <- par[3]
+    rate <- par[4]
+    -sum(actuar::dgenbeta(data, shape1 = shape1, shape2 = shape2,
+                          shape3 = shape3, rate = rate, log = TRUE))
+  }
+
+  # Initial parameter estimates
+  pe <- TidyDensity::util_generalized_beta_param_estimate(x)$parameter_tbl
+  shape1 <- pe$shape1
+  shape2 <- pe$shape2
+  shape3 <- pe$shape3
+  rate <- pe$rate
+  initial_params <- c(shape1 = shape1, shape2 = shape2, shape3 = shape3,
+                      rate = rate)
+
+  # Fit generalized Beta distribution using optim
+  fit_genbeta <- stats::optim(
+    par = initial_params,
+    fn = neg_log_lik_genbeta,
+    data = x
+  )
+
+  # Extract log-likelihood and number of parameters
+  logLik_genbeta <- -fit_genbeta$value
+  k_genbeta <- 4 # Number of parameters for generalized Beta distribution (shape1, shape2, shape3, and rate)
+
+  # Calculate AIC
+  AIC_genbeta <- 2 * k_genbeta - 2 * logLik_genbeta
+
+  # Return AIC
+  return(AIC_genbeta)
+}

docs/pkgdown.yml

@@ -3,7 +3,7 @@ pkgdown: 2.0.9
 pkgdown_sha: ~
 articles:
   getting-started: getting-started.html
-last_built: 2024-05-15T18:50Z
+last_built: 2024-05-15T19:36Z
 urls:
   reference: https://www.spsanderson.com/TidyDensity/reference
   article: https://www.spsanderson.com/TidyDensity/articles