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Computational and Mathematical Methods in Medicine
Volume 2016, Article ID 8727951, 12 pages
http://dx.doi.org/10.1155/2016/8727951
Research Article

Different Estimation Procedures for the Parameters of the Extended Exponential Geometric Distribution for Medical Data

1Statistics Department, Institute of Mathematical and Computer Sciences (ICMC), São Paulo University (USP), 13560-970 São Carlos, SP, Brazil
2Department of Social Medicine, Ribeirão Preto School of Medicine (FMRP), São Paulo University (USP), 14049-900 Ribeirão Preto, SP, Brazil

Received 19 May 2016; Accepted 3 July 2016

Academic Editor: Ezequiel López-Rubio

Copyright © 2016 Francisco Louzada et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We have considered different estimation procedures for the unknown parameters of the extended exponential geometric distribution. We introduce different types of estimators such as the maximum likelihood, method of moments, modified moments, L-moments, ordinary and weighted least squares, percentile, maximum product of spacings, and minimum distance estimators. The different estimators are compared by using extensive numerical simulations. We discovered that the maximum product of spacings estimator has the smallest mean square errors and mean relative estimates, nearest to one, for both parameters, proving to be the most efficient method compared to other methods. Combining these results with the good properties of the method such as consistency, asymptotic efficiency, normality, and invariance we conclude that the maximum product of spacings estimator is the best one for estimating the parameters of the extended exponential geometric distribution in comparison with its competitors. For the sake of illustration, we apply our proposed methodology in two important data sets, demonstrating that the EEG distribution is a simple alternative to be used for lifetime data.