Gumbel distribution

Mathematics

Maximum likelihood

Statistic

Statistics

Extreme value theory

Logistic regression

Estimator

Monte Carlo method

Order statistic

Applied mathematics

Logistic distribution

International Journal of Sciences: Basic and Applied Research

When two distributions have ,approximately ,the  same characteristics, it is often difficult to discriminate between them. In this study, we use the ratio of likelihoods for selecting between the logistic and Gumbel distributions for describing a set of data. The parameters for the logistic and Gumbel distributions are estimated by using maximum likelihood (ML), moments (MOM) and order statistic (OS) methods.  In addition, by using Monte Carlo simulations, discriminating between the two distributions is investigated in terms of the probability of correct selection (PCS) as found based on the different methods of estimation. In general, it is found that the method of ML outperforms all the other methods when the estimators considered are compared in term of efficiency.

Discrimination Between Logistic and Gumbel Distribution