negative binomial

[spsanderson]

#' Estimate Negative Binomial Parameters
#'
#' @family Parameter Estimation
#' @family Binomial
#'
#' @author Steven P. Sanderson II, MPH
#'
#' @details This function will attempt to estimate the negative binomial size and prob
#' 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 beta data.
#'
#' Three different methods of shape parameters are supplied:
#' -  MLE/MME
#' -  MMUE
#'
#' @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_negative_binomial_param_estimate(x)
#'
#' output$parameter_tbl
#'
#' output$combined_data_tbl %>%
#'   ggplot(aes(x = dx, y = dy, group = dist_type, color = dist_type)) +
#'   geom_line() +
#'   theme_minimal() +
#'   theme(legend.position = "bottom")
#'
#' t <- rnbinom(50, 1, .1)
#' util_negative_binomial_param_estimate(t)$parameter_tbl
#'
#' @return
#' A tibble/list
#'
#' @export
#'

util_negative_binomial_param_estimate <- function(.x, .size, 
                                                  .auto_gen_empirical = TRUE){

  # Tidyeval ----
  x_term <- as.numeric(.x)
  sum_x <- sum(x_term, na.rm = TRUE)
  minx <- min(x_term)
  maxx <- max(x_term)
  m <- mean(x_term, na.rm = TRUE)
  n <- length(x_term)
  unique_terms <- length(unique(x_term))
  size = .size
  size_length <- length(size)
  pass <- (n == size_length) || (size_length == 1)

  # Checks ----
  if (!is.vector(x_term, mode = "numeric") || is.factor(x_term) || 
      !is.vector(size, mode = "numeric") || is.factor(size)){
    rlang::abort(
      message = "'.x' and '.size' must be numeric vectors.",
      use_cli_format = TRUE
    )
  }

  if(!pass){
    rlang::abort(
      message = "The length of '.size' must be 1 or the same as the length of '.x'.",
      use_cli_format = TRUE
    )
  }

  if (n > size_length){
    size <- rep(size, n)
  }

  if (n < 1){
    rlang::abort(
      message = "'.x' and '.size' must contain at least one non-missing pari of values.",
      use_cli_format = TRUE
    )
  }

  if(!all(x_term = trunc(x_term)) || any(x_term < 0) || !all(size == trunc(size)) || 
     any(size < 1)){
    rlang::abort(
      message = "All values of '.x' must be non-negative integers, and all values 
      of '.size' must be positive integers.",
      use_cli_format = TRUE
    )
  }

  # Get params ----
  # EnvStats
  size <- sum(size)

  es_mme_size <- size
  es_mme_prob <- size/(size + sum_x)

  es_mvue_size <- size
  es_mvue_prob <- (size - 1)/(size + sum_x - 1)

  # Return Tibble ----
  if (.auto_gen_empirical){
    te <- tidy_empirical(.x = x_term)
    td <- tidy_negative_binomial(.n = n, .size = round(es_mme_size, 3), 
                        .prob = round(es_mme_prob, 3))
    combined_tbl <- tidy_combine_distributions(te, td)
  }

  ret <- dplyr::tibble(
    dist_type = rep('Negative Binomial', 2),
    samp_size = rep(n, 2),
    min = rep(minx, 2),
    max = rep(maxx, 2),
    mean = rep(m, 2),
    method = c("EnvStats_MME_MLE", "EnvStats_MMUE"),
    size = c(es_mme_size, es_mvue_size),
    prob = c(es_mme_prob, es_mvue_prob),
    shape_ratio = c(es_mme_size/es_mme_prob, es_mvue_size/es_mvue_prob)
  )

  # Return ----
  attr(ret, "tibble_type") <- "parameter_estimation"
  attr(ret, "family") <- "negative_binomial"
  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)

}