Generating parameters*of lognormal distribution

[Stephen Okiya]

Dear Stata users,

I am using Stata 17 and would like to simulate a lognormal distribution with parameters as shown below

where E(Y) is average income and G the Gini coefficient of a specific country
The code am using is

local meani = 9791.288442
local gini = 0.59203426 
    
set seed 158961

clear
set obs 18802


gen sigma = sqrt(2)*(1/normal(1))*((`gini' + 1)/2)
gen mu = log(`meani') - (sigma^2)/2
gen lognormal_inc = exp(rnormal(mu, sigma))

mean lognormal_inc
fastgini lognormal_inc

Robust analysis as per the last two commands show that the resulting distribution has biased estimates. My guess is the issue may be arising from how I am generating the inverse standard normal variate.

Any advice would be appreciated.

Thanks in advance

[Tiago Pereira]

Hi, Stephen.

I don't think sigma has been generated correctly, since 1/normal(1) is not the cumulative standard normal distribution. In Stata, (1/normal(1)) means 1.188. Try this:

 
 gen sigma = sqrt(2)*invnormal((`gini' + 1)/2)

[Stephen Okiya]

Thanks so much Tiago Pereira Your suggestion works!!