#' Estimate Triangular Parameters
#'
#' @family Parameter Estimation
#' @family Triangular
#'
#' @author Steven P. Sanderson II, MPH
#'
#' @details This function will attempt to estimate the triangular min, mode, and max
#' parameters given some vector of values.
#'
#' @description This function will attempt to estimate the triangular min, mode, and max
#' parameters given some vector of values.
#'
#' 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 beta data.
#'
#' @param .x The vector of data to be passed to the function. Must be numeric, and
#' all values must be 0 <= x <= 1
#' @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 `$combined_data_tbl` from the function output.
#'
#' @examples
#' library(dplyr)
#' library(ggplot2)
#'
#' x <- mtcars$mpg
#' output <- util_triangular_param_estimate(x)
#'
#' output$parameter_tbl
#'
#' output$combined_data_tbl |>
#'   tidy_combined_autoplot()
#'
#' params <- tidy_triangular()$y |>
#'   util_triangular_param_estimate()
#' params$parameter_tbl
#' 
#' @return
#' A tibble/list
#' 
#' @name util_triangular_param_estimate
NULL
#'
#' @export
#' @rdname util_triangular_param_estimate

util_triangular_param_estimate <- function(.x, .auto_gen_empirical = TRUE) {
  
  # Tidyeval ----
  x_term <- as.numeric(.x)
  minx <- min(x_term)
  maxx <- max(x_term)
  n <- length(x_term)
  
  # Checks ----
  if (n < 3) {
    rlang::abort(
      message = "The data must have at least three (3) unique data points.",
      use_cli_format = TRUE
    )
  }
  
  if (!is.numeric(x_term)) {
    rlang::abort(
      "The '.x' parameter must be numeric."
    )
  }
  
  # Get params ----
  a <- min(x_term)
  c <- max(x_term)
  b <- 3*mean(x_term) - max(x_term) - min(x_term)
  
  
  # Return Tibble ----
  if (.auto_gen_empirical) {
    te <- tidy_empirical(.x = x_term)
    td <- tidy_triangular(.n = n, .min = round(a, 3), .mode = round(b, 3), .max = round(c, 3))
    combined_tbl <- tidy_combine_distributions(te, td)
  }
  
  ret <- dplyr::tibble(
    dist_type = "Triangular",
    samp_size = n,
    min = minx,
    max = maxx,
    mode = c,
    method = "Basic"
  )
  
  # Return ----
  attr(ret, "tibble_type") <- "parameter_estimation"
  attr(ret, "family") <- "triangular"
  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)
}

> library(dplyr)
> library(ggplot2)
> 
> x <- mtcars$mpg
> output <- util_triangular_param_estimate(x)
> 
> output$parameter_tbl
# A tibble: 1 × 6
  dist_type  samp_size   min   max  mode method
  <chr>          <int> <dbl> <dbl> <dbl> <chr> 
1 Triangular        32  10.4  33.9  33.9 Basic 
> 
> output$combined_data_tbl |>
+   tidy_combined_autoplot()
> 
> params <- tidy_triangular()$y |>
+   util_triangular_param_estimate()
> params$parameter_tbl
# A tibble: 1 × 6
  dist_type  samp_size    min   max  mode method
  <chr>          <int>  <dbl> <dbl> <dbl> <chr> 
1 Triangular        50 0.0997 0.805 0.805 Basic