How can i simulate a lognormal distribution without knowing mean and standard deviation?

Question

Consider the Lucas endowment economy with inflation, we know that consumption growth and inflation are log-normally distributed,and that consumption growth and inflation are uncorrelated through time and with each other.
How can I compute Compute the one period nominal risk free rate (1 + it,t+1)?

I have to solve this problem through matlab and tried using

lognrnd()
g_t1 = lognrnd(mu_c, sg_c1)
g_t2 = lognrnd(mu_c, sg_c2)
pi_t1 = lognrnd(mu_pi, sg_pi)
pi_t2 = lognrnd(mu_pi, sg_pi)

but I don't know how to go on without any values. How can I then assign the distribution values to a vector or matrix?

Answer 1

You can’t generate simulated values from a distribution without providing a concrete parameterization for that distribution.

If you can’t use theory to determine the parameter values but you have access to observational data, you can estimate the parameter values. Alternatively, you can use subject matter opinions for your problem context, or WAGs (Wild-Assed Guesses). In all of these cases, be aware that the true parameter values almost certainly differ from the values you are using. Consequently, I recommend using design of experiments over plausible ranges of the values, and fitting a response surface model to determine how sensitive your simulation’s results are to variation in the input distribution’s parameters.