Convert normal random variable into beta random variable in STATA

Question

I need to generate two random variables - lognormal and beta distributed - while ensuring that the correlation between the two variables is -0.3.

I generated two normal random variables with -0.3 correlation as follows;

matrix C = (1, -0.3 \ -0.3, 1)
drawnorm x y, mean(0.921, 0) sds(0.174,1) corr(C)
// Here x is normal rv with mean 0.921 and sd 0.174 while y is a standard normal rv. 

Converting x to lognormal is simple. I do this

gen price = exp(x)
// price is now the lognormal(0.921, 0.174)

Problem is in converting y~$N(0,1)$ to $beta(\alpha,\beta)$. Is there a way to do it?

Answer 1

This is how I was able to generate these variables;

matrix      C = (1, -0.32 \ -0.32, 1) // Matrix defining the correlation between two vars
drawnorm    x y, mean(0.921, 0) sds(0.174,1) corr(C) // Generate two multivariate normal vars with specified dependency
// Here x is normal rv with mean 0.921 and sd 0.174 while y is a standard normal rv. 

Converting x to lognormal is simple. I do this

gen price = exp(x)
// price is now the lognormal(0.921, 0.174)

To convert y (a standard normal rv) I generated a normal cdf of y as follows;

gen         z2 = normal(y)

Then I used invibeta function to generate beta density with parameters a and b as follows;

gen yield = invibeta(a, b, z2)

The above process generates price (lognormal) and yield (beta) with correlation of -0.30.