sweness_kurtosis_plots.r

# Plot histogram and normal curve for (simulated) data

library(tidyverse)
library(moments)
library(glue)

plot_distribution = function (x) {
  m = mean(x)
  sd = sd(x)
  skewness=skewness(x)
  kurtosis=kurtosis(x)
  
  tibble(x=round(x)) |> 
    ggplot() + 
    geom_bar(aes(x), fill="darkgrey") + 
    stat_function(fun=function(...) dnorm(...) * length(x), n=100, args=list(mean=m, sd=sd)) +
    scale_y_continuous("Frequency of simulated data", 
                       sec.axis = sec_axis(~ . / length(x), name = "Density for normal distribution")) +
    labs(
      title="Histogram of (simulated) data with estimated normal curve superimposed",
      subtitle=glue("Mean: {round(m,2)}, sd: {round(sd,2)}, skewness: {round(skewness,2)}, kurtosis: {round(kurtosis, 2)}"))
}

# Normal distribution
x <- rnorm( 5000, 0, 2 )
plot_distribution(x)

# Skew right by moving some points over
x <- rnorm( 5000, 0, 2 )
flip =runif(length(x)) > .75
x = ifelse(flip & x<0, x*-1, x)

# leptokurtic by adding an extra weight near the peak
x = c(
  rnorm( 5000, 0, 4 ),
  rnorm( 2000, 0, 1 ))
plot_distribution(x)

# platokurtic by adding extra weight in the middle regions
x = c(
  rnorm( 5000, 0, 4 ),
  rnorm( 1000, 4, 2.5 ),
  rnorm( 1000, -4, 2.5 )
  )
plot_distribution(x)


# leptokurtic and skewed by adding an extra weight near the peak on the side
x = c(
  rnorm( 5000, 0, 4 ),
  rnorm( 2000, 1, 2 ))
plot_distribution(x)