Estimation based on minimum distance between empirical and theoretical distribution functions

Marjan JALILIAN, Maryam SHARIFDOUST
1.591 798

Abstract


Abstract. Distribution function, other than goodness-of-fit test, is also used in point estimation approach, especially in distributions with closed-form distribution functions. In this paper, the goal is to estimate parameters with minimum distance between empirical and theoretical distribution functions by means of Hellinger and Jeffrey distance measures. Monte Carlo simulation for estimating parameters of generalized Pareto distribution with three parameters represents acceptable results. This distribution does not have any close form moment for obtaining MME and also the estimation of parameters by MLE needs some numerical ways. Finally, the introduced methods is implemented to real data and compared to classical estimators.


Keywords


Method of Moment, Maximum Likelihood, Hellinger Distance, Jeffrey Distance, Monte Carlo

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