Fixes #474

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_pareto_aic)
+export(util_generalized_pareto_param_estimate)
+export(util_generalized_pareto_stats_tbl)
 export(util_geometric_aic)
 export(util_geometric_param_estimate)
 export(util_geometric_stats_tbl)

NEWS.md

@@ -36,6 +36,9 @@ Add Function `util_inverse_pareto_stats_tbl()` to create a summary table of the
 12. Fix #475 - Add function `util_inverse_burr_param_estimate()` to estimate the parameters of the Inverse Gamma distribution.
 Add function `util_inverse_burr_aic()` to calculate the AIC for the Inverse Gamma distribution.
 Add function `util_inverse_burr_stats_tbl()` to create a summary table of the Inverse Gamma distribution.
+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.
 
 ## Minor Improvements and Fixes
 1. Fix #468 - Update `util_negative_binomial_param_estimate()` to add the use of

R/est-param-gen-pareto.R

@@ -0,0 +1,132 @@
+#' Estimate Generalized Pareto Parameters
+#'
+#' @family Parameter Estimation
+#' @family Generalized Pareto
+#'
+#' @author Steven P. Sanderson II, MPH
+#'
+#' @details This function will attempt to estimate the generalized Pareto shape1, shape2, 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 Pareto 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 `$combined_data_tbl` from the function output.
+#'
+#' @examples
+#' library(dplyr)
+#' library(ggplot2)
+#'
+#' set.seed(123)
+#' x <- tidy_generalized_pareto(100, .shape1 = 1, .shape2 = 2, .scale = 3)[["y"]]
+#' output <- util_generalized_pareto_param_estimate(x)
+#'
+#' output$parameter_tbl
+#'
+#' output$combined_data_tbl %>%
+#'   tidy_combined_autoplot()
+#'
+#' @return
+#' A tibble/list
+#'
+#' @name util_generalized_pareto_param_estimate
+NULL
+
+#' @export
+#' @rdname util_generalized_pareto_param_estimate
+
+util_generalized_pareto_param_estimate <- function(.x, .auto_gen_empirical = TRUE) {
+
+  # Tidyeval ----
+  x_term <- as.numeric(.x)
+  n <- length(x_term)
+
+  # Checks ----
+  if (!is.vector(x_term, mode = "numeric") || is.factor(x_term)) {
+    rlang::abort(
+      message = "'.x' must be a numeric vector.",
+      use_cli_format = TRUE
+    )
+  }
+
+  if (n < 2 || any(x_term <= 0)) {
+    rlang::abort(
+      message = "'.x' must contain at least two non-missing distinct values. All values of '.x' must be positive.",
+      use_cli_format = TRUE
+    )
+  }
+
+  # Negative log-likelihood function for generalized Pareto distribution
+  genpareto_lik <- function(params, data) {
+    shape1 <- params[1]
+    shape2 <- params[2]
+    scale <- params[3]
+    -sum(actuar::dgenpareto(data, shape1 = shape1, shape2 = shape2, scale = scale, log = TRUE))
+  }
+
+  # Initial parameter guesses
+  initial_params <- c(shape1 = 1, shape2 = 1, scale = 1)
+
+  # Optimize to minimize the negative log-likelihood
+  opt_result <- optim(
+    par = initial_params,
+    fn = genpareto_lik,
+    data = x_term,
+    method = "L-BFGS-B",
+    lower = c(1e-5, 1e-5, 1e-5)
+  )
+
+  shape1 <- opt_result$par[1]
+  shape2 <- opt_result$par[2]
+  scale <- opt_result$par[3]
+  rate <- 1 / scale
+
+  # Return Tibble ----
+  if (.auto_gen_empirical) {
+    te <- tidy_empirical(.x = x_term)
+    td <- tidy_generalized_pareto(
+      .n = n,
+      .shape1 = round(shape1, 3),
+      .shape2 = round(shape2, 3),
+      .rate = round(rate, 3)
+    )
+    combined_tbl <- tidy_combine_distributions(te, td)
+  }
+
+  ret <- dplyr::tibble(
+    dist_type = "Generalized Pareto",
+    samp_size = n,
+    min = min(x_term),
+    max = max(x_term),
+    mean = mean(x_term),
+    shape1 = shape1,
+    shape2 = shape2,
+    rate = rate,
+    scale = scale
+  )
+
+  # Return ----
+  attr(ret, "tibble_type") <- "parameter_estimation"
+  attr(ret, "family") <- "generalized_pareto"
+  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-pareto-tbl.R

@@ -0,0 +1,85 @@
+#' Distribution Statistics
+#'
+#' @family Generalized Pareto
+#' @family Distribution Statistics
+#'
+#' @author Steven P. Sanderson II, MPH
+#'
+#' @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)
+#'
+#' tidy_generalized_pareto() |>
+#'   util_generalized_pareto_stats_tbl() |>
+#'   glimpse()
+#'
+#' @return
+#' A tibble
+#'
+#' @name util_generalized_pareto_stats_tbl
+NULL
+#' @export
+#' @rdname util_generalized_pareto_stats_tbl
+util_generalized_pareto_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)$tibble_type != "tidy_generalized_pareto") {
+    rlang::abort(
+      message = "You must use 'tidy_generalized_pareto()'",
+      use_cli_format = TRUE
+    )
+  }
+
+  # Data
+  data_tbl <- dplyr::as_tibble(.data)
+
+  atb <- attributes(data_tbl)
+  shape1 <- atb$.shape1
+  shape2 <- atb$.shape2
+  rate <- atb$.rate
+  scale <- 1 / rate
+
+  stat_mean <- ifelse(shape1 <= 1, Inf, scale * shape1 / (shape1 - 1))
+  stat_mode <- scale * (shape1 - 1) / shape1
+  stat_median <- scale * actuar::qgenpareto(0.5, shape1 = shape1, shape2 = shape2, scale = scale)
+  stat_var <- ifelse(shape1 <= 2, Inf, (scale^2 * shape1) / ((shape1 - 1)^2 * (shape1 - 2)))
+  stat_skewness <- ifelse(shape1 <= 3, "undefined", 2 * (1 + shape1) / (shape1 - 3) * sqrt((shape1 - 2) / shape1))
+  stat_kurtosis <- ifelse(shape1 <= 4, "undefined", 6 * (shape1^3 + shape1^2 - 6 * shape1 - 2) / (shape1 * (shape1 - 3) * (shape1 - 4)))
+
+  # 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,
+    median = stat_median,
+    coeff_var = 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-pareto.R

@@ -0,0 +1,84 @@
+#' Calculate Akaike Information Criterion (AIC) for Generalized Pareto Distribution
+#'
+#' This function calculates the Akaike Information Criterion (AIC) for a generalized Pareto distribution fitted to the provided data.
+#'
+#' @family Utility
+#'
+#' @author Steven P. Sanderson II, MPH
+#'
+#' @description
+#' This function estimates the shape1, shape2, and rate parameters of a generalized 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 generalized Pareto distribution.
+#'
+#' @details
+#' This function fits a generalized Pareto distribution to the provided data using maximum
+#' likelihood estimation. It estimates the shape1, shape2, and rate parameters
+#' of the generalized 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 shape1, shape2, and rate parameters of the generalized 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 <- actuar::rgenpareto(100, shape1 = 1, shape2 = 2, scale = 3)
+#' util_generalized_pareto_aic(x)
+#'
+#' @return
+#' The AIC value calculated based on the fitted generalized Pareto distribution to the provided data.
+#'
+#' @name util_generalized_pareto_aic
+NULL
+
+#' @export
+#' @rdname util_generalized_pareto_aic
+util_generalized_pareto_aic <- function(.x) {
+  # Tidyeval
+  x <- as.numeric(.x)
+
+  # Negative log-likelihood function for generalized Pareto distribution
+  neg_log_lik_genpareto <- function(par, data) {
+    shape1 <- par[1]
+    shape2 <- par[2]
+    scale <- par[3]
+    -sum(actuar::dgenpareto(data, shape1 = shape1, shape2 = shape2, scale = scale, log = TRUE))
+  }
+
+  # Initial parameter estimates
+  pe <- TidyDensity::util_generalized_pareto_param_estimate(x)$parameter_tbl
+  shape1_init <- pe$shape1
+  shape2_init <- pe$shape2
+  scale_init <- pe$scale
+  initial_params <- c(shape1 = shape1_init, shape2 = shape2_init, scale = scale_init)
+
+  # Fit generalized Pareto distribution using optim
+  fit_genpareto <- stats::optim(
+    par = initial_params,
+    fn = neg_log_lik_genpareto,
+    data = x,
+    method = "L-BFGS-B",
+    lower = c(1e-5, 1e-5, 1e-5)
+  )
+
+  # Extract log-likelihood and number of parameters
+  logLik_genpareto <- -fit_genpareto$value
+  k_genpareto <- 3 # Number of parameters for generalized Pareto distribution (shape1, shape2, and scale)
+
+  # Calculate AIC
+  AIC_genpareto <- 2 * k_genpareto - 2 * logLik_genpareto
+
+  # Return AIC
+  return(AIC_genpareto)
+}

docs/pkgdown.yml

@@ -3,7 +3,7 @@ pkgdown: 2.0.9
 pkgdown_sha: ~
 articles:
   getting-started: getting-started.html
-last_built: 2024-05-15T18:03Z
+last_built: 2024-05-15T18:50Z
 urls:
   reference: https://www.spsanderson.com/TidyDensity/reference
   article: https://www.spsanderson.com/TidyDensity/articles