r/element 3.Rmd at master · north-tower/r · GitHub

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---
title: "Element 3"
output: html_notebook
---


```{r}
df <- read.csv("Attachment_1638128243.csv", header=TRUE)
df
#NAS
df[is.na(df)] = 0

#Percentile
quantile(df,.7,na.rm=TRUE)

#Mean
mean.result = mean(df$Claim.size)
#stadard deviation
sd.result = sqrt(var(df$Claim.size))

#simulation
set.seed(5)

# normal
x <- rnorm(1000, mean.result, sd.result)

#Skewness and Kurtosis
library(moments)
skewness(x)

kurtosis(x)

#Skewness
library(ggplot2)
datasim <- data.frame(x)
density_plot <-
  datasim %>%
  ggplot(aes(x = x)) +
  stat_density(geom = "line", alpha = 1, colour = "cornflowerblue")

density_plot

shaded_area_data <-
  ggplot_build(density_plot)$data[[1]] %>%
  filter(x < mean(datasim$x))

density_plot_shaded <-
  density_plot +
  geom_area(data = shaded_area_data, aes(x = x, y = y), fill="pink", alpha = 0.5)

density_plot_shaded

median <- median(datasim$x)
mean <- mean(datasim$x)

median_line_data <-
  ggplot_build(density_plot)$data[[1]] %>%
  filter(x <= median)

density_plot_shaded +

  geom_segment(data = shaded_area_data, aes(x = mean, y = 0, xend = mean, yend = density),
               color = "red", linetype = "dotted") +

  geom_segment(data = median_line_data, aes(x = median, y = 0, xend = median, yend = density),
               color = "black", linetype = "dotted") +
  ggtitle("Density Plot Illustrating Skewness")


#Kurtosis
library(tidyverse)
mean <- mean(datasim$x)

sd_pos <-  mean + (2 * sd(datasim$x))

sd_neg <- mean - (2 * sd(datasim$x))

sd_pos_shaded_area <-
  ggplot_build(density_plot)$data[[1]] %>%
  filter(x > sd_pos )

sd_neg_shaded_area <-
  ggplot_build(density_plot)$data[[1]] %>%
  filter(x < sd_neg)

density_plot <-
    density_plot +
    geom_area(data = sd_pos_shaded_area, aes(x = x, y = y), fill="pink", alpha = 0.5) +
    geom_area(data = sd_neg_shaded_area, aes(x = x, y = y), fill="pink", alpha = 0.5) +
    scale_x_continuous(breaks = scales::pretty_breaks(n = 10))

density_plot

mean <- mean(datasim$x)

mean_line_data <-
  ggplot_build(density_plot)$data[[1]] %>%
  filter(x <= mean)

density_plot + geom_segment(data = median_line_data, aes(x = median, y = 0, xend = median, yend = density),
               color = "black", linetype = "dotted")+
  ggtitle("Density Plot Illustrating Kurtosis")


```
The critical value of Zg2 is approximately 2. (This is a two-tailed test of excess kurtosis ≠ 0 at approximately the 0.05 significance level.)