normal_distributions.R

library(tidyverse)
theme_set(theme_classic())

plot_normal <- function(mean = 0, sd = 1, xmin = -3, xmax = 3) {
  tibble(x = seq(xmin, xmax, length.out = 1000),
         d = dnorm(x, mean = mean, sd = sd)) %>% 
    ggplot(aes(x = x, y = d)) + geom_line() + 
    geom_segment(x = mean, 
                 xend = mean, 
                 y = 0, 
                 yend = dnorm(mean, mean, sd), colour = 'grey') +
    geom_segment(x = mean, 
                 xend = mean + sd, 
                 y = dnorm(mean, mean, sd)/2, 
                 yend = dnorm(mean, mean, sd)/2, colour = 'grey')
  
}

normal_percentiles <- function(mean = 0, sd = 1){
  c(`0.005` = qnorm(0.005, mean = mean, sd = sd),
    `0.025` = qnorm(0.025, mean = mean, sd = sd),
    `0.25` = qnorm(0.25, mean = mean, sd = sd),
    `0.5` = qnorm(0.5, mean = mean, sd = sd),
    `0.75` = qnorm(0.75, mean = mean, sd = sd),
    `0.975` = qnorm(0.975, mean = mean, sd = sd),
    `0.995` = qnorm(0.995, mean = mean, sd = sd))
}

plot_normal_sample <- function(n = 1000, mean = 0, sd = 1, bins = 10){
  tibble(x = rnorm(n, mean, sd)) %>% 
    ggplot(aes(x = x)) + geom_histogram(bins = bins, colour = 'white')
}

plot_repeat_normal_samples <- function(N = 1000, n = 10, mean = 0, sd = 1){
  df <- map(seq(N), 
            ~rnorm(n, mean = mean, sd = sd) %>% 
              enframe() %>% 
              summarize(mean = mean(value), stdev = sd(value))
  ) %>% bind_rows() %>% 
    rownames_to_column(var = 'id') %>% 
    mutate(id = as.numeric(id))
  
  ggplot(df,
         aes(x = id, y = mean)) + 
    geom_point() + 
    geom_hline(yintercept = mean, colour = 'red') + 
    ylim(mean - sd * 2, mean + sd * 2)
}

hist_repeat_normal_samples <- function(N = 1000, n = 10, mean = 0, sd = 1, bins = 25){
  df <- map(seq(N), 
            ~rnorm(n, mean = mean, sd = sd) %>% 
              enframe() %>% 
              summarize(mean = mean(value), stdev = sd(value))
  ) %>% bind_rows() %>% 
    rownames_to_column(var = 'id') %>% 
    mutate(id = as.numeric(id))
  
  ggplot(df,
         aes(x = mean)) + 
    geom_histogram(bins = bins, colour = 'white')
}