ACTU-457 (Mast 724) Risk Theory

library(moments)
plot(cars)

x <- cars[,1]
n <- length(x)
(emp_average <- sum(x)/n)

[1] 15.4

mean(x)

[1] 15.4

(emp_var <- sum((x-emp_average)^2)/n)

[1] 27.4

(unbiased_var <- emp_var*n/(n-1))

[1] 27.95918

var(x)

[1] 27.95918

(emp_skew <- (sum((x-emp_average)^3)/n)/emp_var^(3/2))

[1] -0.1139548

skewness(x)

[1] -0.1139548

(emp_kurtosis <- (sum((x-emp_average)^4)/n)/emp_var^2)

[1] 2.422853

kurtosis(x)

[1] 2.422853