Generalized entropy optimization distributions dependent on parameter in time series

Abstract

In this paper, we have proposed Generalized Entropy Optimization Problems (GEOP) concerned with parameters which consist of maximizing Entropy Functional subject to constraints dependent on parameters. Therefore, MinMaxEnt and MaxMaxEnt distributions are obtained as solutions of these problems. On bases of MinMaxEnt distribution we have developed a new estimation method of obtaining missing values in time series. Mentioned estimation method is applied to the data generated from autoregressive model for one missing value. The performance of the developed method is evaluated by mean square errors (MSE) calculated from simulation studies and the validity of this method is shown.