Question

Tail Moments of the Standard Normal Distribution. Your goal is to estimate the following conditional moment of the standard normal distribution: Z~N(0,1) (a) Write an R function that takes inputs n (sample size) and a > 0 and estimates θα using an accept/reject approach. For this part, draw proposals from a standard normal.

Answer 1

R-Code

#Defining the function

tail_moments=function(n,alpha)
{

z=rnorm(n)                             #Taking random sample from N(0,1)      
pos=which(z>alpha)              #Finding the position of varaibles having value > alpha
z_alpha=z[pos]                       #Selecting the numbers
theta_alpha=mean(z_alpha) #Finding the conditional mean
return(theta_alpha)                 #Returning the value
}

t=tail_moments(10000,0)        #Calling the function tail_moments