r basiscs3

rm(list = ls())
library(tidyverse)
library(R6)

# datastes ------
set.seed(1)
population1 = tibble(x = rnorm(20.00, 20, 5),
                     y = rnorm(20.00, 15, 5),)
population2 = tibble(x = rpois(3231, 50),
                     y = rnorm(3231, 45),)
population3 = tibble(x = runif(8512, 20, 100),
                     y = runif(8512, 18, 155))
proj = R6Class(
  public = list(
    x = NA,
    y = NA,
    n = NA,
    initialize = function(x, y, n) {
      self$x = x
      self$y = y
      self$n = n
    },
    pop_var = function(x) {
      x_xbar =  (x - mean(x)) ^ 2 %>% sum()
      res = x_xbar / (length(x) - 1)
      return(res)
    },
    beta1 = function(S_x) {
      x = self$x
      num = (sum((x - mean(x)) ^ 3) * length(x))
      den = ((length(x) - 1) * (length(x) - 2) * S_x ^ 3)
      beta = num / den
      return(beta)
    },
    beta2 = function(S_x) {
      x = self$x
      num1 = length(x) * (length(x) + 1) * sum((x - mean(x)) ^ 4)
      den1 = ((length(x) - 1) * (length(x) - 2) * (length(x) - 3)) * S_x ^
        4
      num2 = 3 * (length(x) - 1) ^ 2
      den2 = ((length(x) - 2) * (length(x) - 3))
      
      beta = (num1 / den1)#-(num2/den2)
      
      return(beta)
    },
    t_m = function() {
      quartiles = quantile(self$x) %>%
        as_tibble() %>%
        rowid_to_column() %>%
        filter(rowid %in% 2:4) %>%
        mutate(rowid = paste0("Q_", rowid - 1))
      Q1 = quartiles %>% filter(rowid == "Q_1") %>% pull(value)
      Q2 = quartiles %>% filter(rowid == "Q_2") %>% pull(value)
      Q3 = quartiles %>% filter(rowid == "Q_3") %>% pull(value)
      T_m = (Q1 + 2 * Q2 + Q3) / 4
      return(T_m)
    },
    M_r = function() {
      x = self$x
      mr = (min(x) + max(x)) / 2
      return(mr)
    },
    QD = function() {
      quartiles = quantile(self$x) %>%
        as_tibble() %>%
        rowid_to_column() %>%
        filter(rowid %in% 2:4) %>%
        mutate(rowid = paste0("Q_", rowid - 1))
      Q1 = quartiles %>% filter(rowid == "Q_1") %>% pull(value)
      Q2 = quartiles %>% filter(rowid == "Q_2") %>% pull(value)
      Q3 = quartiles %>% filter(rowid == "Q_3") %>% pull(value)
      qd = (Q3 - Q1) / 2
      return(qd)
    },
    G = function() {
      N = length(self$x)
      # sum loop
      tot = list()
      for (i in 1:N) {
        rec = (((2 * i) - N - 1) / (2 * N)) * self$x[i]
        tot = append(tot, rec)
      }
      est = (4 / (N - 1)) * sum(unlist(tot))
      return(est)
    },
    Sp_w = function() {
      N = length(self$x)
      tot = 0
      for (i in 1:N) {
        rec = (2 * i - N - 1) * self$x[i]
        tot= rec + tot
      }
      res = (sqrt(pi)/(N^2))*tot
      return(res)
    },
    estimates = function() {
      out = tibble(
        N = length(self$x),
        n = self$n,
        Y_bar = mean(self$y),
        X_bar = mean(self$x),
        S_y = sqrt(self$pop_var(x = self$y)),
        C_y = sqrt(self$pop_var(x = self$y)) / mean(self$y),
        S_x = sqrt(self$pop_var(x = self$x)),
        C_x = sqrt(self$pop_var(x = self$x)) / mean(self$x),
        beta1 = self$beta1(S_x),
        beta2 = self$beta2(S_x),
        M_d = median(self$x),
        T_m = self$t_m(),
        M_r = self$M_r(),
        QD = self$QD(),
        G = self$G(),
        Sp_w = self$Sp_w()
      ) %>% t() %>%
        as_tibble(rownames = "Parameter")
      return(out)
    }
  )
)
# x = c(9, 10, 12, 15, 25, 30, 35, 40, 50, 50, 50, 100, 100, 150, 250)
# pop1$Sp_w() %>% unlist()
pop1 = proj$new(x = population1$x, y = population1$y, n = 20)
pop2 = proj$new(x = population2$x, y = population2$y, n = 20)
pop3 = proj$new(x = population3$x, y = population3$y, n = 50)



results = pop1$estimates() %>%
  left_join(pop2$estimates(), by = 'Parameter') %>%
  left_join(pop3$estimates(), by = 'Parameter') %>%
  mutate_if(is.numeric, round, 4)
colnames(results) = c('Parameter', paste0("Population_", 1:3))
writexl::write_xlsx(results, "results.xlsx")