Question

A random variable Y follows Gumbel distribution, the CDF of which is: ?(? ≤ ?) = ?^−?^−?. Simulate 10 random numbers from this distribution using the LCG: Xi = (171*X0 + 24316) mod 30269 where the seed value (X0) is 1914. Show necessary calculations

Answer 1

Using the seed, we compute the following random numbers and the uniform random numbers (in (0,1)) using the relation that

uniform random number(u)=random number/30269.

Now equating Gumbel CDF with u, we get the sample y from Gumbel distribution as y=-log(-log(u)).

All these are computed in the following table:

For query in above, comment.