t

[spsanderson]

https://www.itl.nist.gov/div898/handbook/eda/section3/eda3664.htm

[spsanderson]

Function:

#' Distribution Statistics
#' 
#' @family T Distribution
#' @fmaily Distribution Statistics
#' 
#' @author Steven P. Sanderson II, MPH
#' 
#' @details This function will take in a tibble and returns 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 
#' tidy_cauchy() %>%
#'   util_cauchy_stats_tbl()
#' 
#' @return 
#' A tibble
#' 
#' @export
#' 

util_t_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_t"){
    rlang::abort(
      message = "You must use 'tidy_t()'",
      use_cli_format = TRUE
    )
  }

  # Data
  data_tbl <- tibble::as_tibble(.data)

  atb <- attributes(data_tbl)

  stat_mean   <- 0
  stat_median <- 0
  stat_mode   <- 0
  stat_sd     <- ifelse(atb$.df > 2, sqrt( (atb$.df / (atb$.df - 1)) ), "undefined")
  stat_coef_var <- "undefined"
  stat_skewness <- 0
  stat_kurtosis <- ifelse(atb$.df > 4, (3*(atb$.df - 2) / (atb$.df - 4)), "undefined")

  # Data Tibble
  ret <- tibble::tibble(
    tidy_function = atb$tibble_type,
    function_call = atb$dist_with_params,
    distribution = atb$tibble_type %>% 
      stringr::str_remove("tidy_") %>% 
      stringr::str_to_title(),
    distribution_type = atb$distribution_family_type,
    points = atb$.n,
    simulations = atb$.num_sims,
    mean = stat_mean,
    median = stat_median,
    mode = stat_mode,
    std_dv = stat_sd,
    coeff_var = stat_coef_var,
    skewness = stat_skewness,
    kurtosis = stat_kurtosis,
    computed_std_skew = tidy_skewness_vec(data_tbl$y),
    computed_std_kurt = tidy_kurtosis_vec(data_tbl$y)
  )

  # Return
  return(ret)

}

Examples:

tidy_t() %>% 
  util_t_stats_tbl() %>%
  glimpse()

util_t_stats_tbl(rt(50))

util_t_stats_tbl(tidy_uniform())