The Beta Distribution

Getting familiar with the basic properties of the beta distribution

library(dplyr)

## 
## Attaching package: 'dplyr'
## 
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## 
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(ggplot2)
library(e1071)

alpha <- 600
beta <- 400
s1 <- rbeta(1000, alpha, beta)
ggplot(data.frame(s1), aes(x=s1)) + geom_freqpoly()

## stat_bin: binwidth defaulted to range/30. Use 'binwidth = x' to adjust this.

sum(s1)/length(s1)

## [1] 0.6002

mean(s1)  # this is computed in cov.c, hence different rounding than above

## [1] 0.6002

alpha/(alpha+beta)

## [1] 0.6

sum((s1 - mean(s1))^2)/length(s1)

## [1] 0.000249

var(s1)

## [1] 0.0002493

(alpha*beta)/((alpha+beta)**2*(alpha + beta + 1))

## [1] 0.0002398

skewness(s1)

## [1] -0.1312