Question

The normal distribution has parameters μ and σ. The possible values for μ are all numbers on the real line, while σ must be positive. Write an R function that takes in a vector with two elements theta(whose values are unrestricted) and returns a list with two elements. The first element is to represents μ,mu=theta[1], and the second element is to represent σ,sigma=exp(theta[2]). Write a function that takes in a named list for mu and sigma and returns theta.

Answer 1

## "Unrestricted_Theta()" is the R function that takes in a vector with two elements theta
## (whose values are unrestricted)

Unrestricted_Theta <- function(theta){
   mu <- theta[1];
   sigma <- exp(theta[2]);
   theta <- list();           ### Defining a list named as theta
   theta[[1]] <- mu;           ### Assigning mu to list theta as the first element
   theta[[2]] <- sigma;       ### Assigning sigma to list theta as the second element
   return(theta);
}