options(warn=-1)

Beta Distribution The Beta Distribution is commonly used distribution for a continous random variable that only take values betweeen 0 <= x <= 1

it has a probability density function g(x;a,b) ==> k(x^(a-1))((1-x)^(b-1)) for 0<= x <=1

the shape of the curve is determined by (x^(a-1))((1-x)^(b-1)) and k is the constant to make this equation probabaility density function

k (constant) is generalization of factorial function Fact(a+b)/Fact(a)Fact(b)

• so lets create probability density function for beta distribution*

beta<-function(x,a,b){
  betaf<-(factorial(a+b)/(factorial(a)*factorial(b)))*(x^(a-1))*((1-x)^(b-1))
  return(betaf)
}

lets create a variable that ranges between 0 and 1

x <- seq(0, 1, length = 21)

define a and b values

a_b <- c(0.5,1,2,3,4,5)

plot probability densities with loop

dist<-NULL
for (a in a_b){
  for (b in a_b){
    dist<- beta(x,a,b)
    plot(x,dist,type="b",col="blue",main = paste("Beta (",a,",",b,")"),ylab="density")
  }
}

Thanks: Hincal Topcuoglu