I know mean and variance of a skewed positive random variable $X$ analytically. in literature both gamma and log-normal distributions can be fitted to such a random variable. I know that to find the best fitted distribution, maximum likelihood estimators can be used. but for that, I must run monte carlo simulations. I can estimate gamma or log-normal distributions by mean and variance which I know analytically. By monte carlo, I know that these estimated distributions, have enough accuracy and gamma distribution is better fitted.

Actually, I need 95th percentile of the random variable. I can estimate it by fitted distributions (gamma or log-normal). I prefer to use the distribution with larger 95th percentile (because I need to study the worst case, and I do not want to use MCS. I must study large numbers of different situations and perform MCS for each, but I can calculate mean and variance of each one analytically.)

I can prove that kurtosis of estimated gamma distribution is smaller than estimated log-normal distribution if both are estimated using known variance and mean. also, MCS shows that 95th percentile of estimated gamma distribution is more accurate and is larger than estimated log-normal distribution.

Is it possible to prove that 95th percentile of estimated gamma distribution is larger than estimated log-normal where mean and variance of both are the same (kurtosis can help?)?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.