Estimation of the Parameters of the Reversed Generalized Logistic Distribution with Progressive Censoring Data

The reversed generalized logistic (RGL) distributions are very useful classes of densities as they posses a wide range of indices of skewness and kurtosis. This paper considers the estimation problem for the parameters of the RGL distribution based on progressive Type II censoring. The maximum like...

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Main Authors: Z. A. Abo-Eleneen, E. M. Nigm
Format: Article
Language:English
Published: Wiley 2010-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2010/539860
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author Z. A. Abo-Eleneen
E. M. Nigm
author_facet Z. A. Abo-Eleneen
E. M. Nigm
author_sort Z. A. Abo-Eleneen
collection DOAJ
description The reversed generalized logistic (RGL) distributions are very useful classes of densities as they posses a wide range of indices of skewness and kurtosis. This paper considers the estimation problem for the parameters of the RGL distribution based on progressive Type II censoring. The maximum likelihood method for RGL distribution yields equations that have to be solved numerically, even when the complete sample is available. By approximating the likelihood equations, we obtain explicit estimators which are in approximation to the MLEs. Using these approximate estimators as starting values, we obtain the MLEs using iterative method. We examine numerically MLEs estimators and the approximate estimators and show that the approximation provides estimators that are almost as efficient as MLEs. Also we show that the value of the MLEs decreases as the value of the shape parameter increases. An exact confidence interval and an exact joint confidence region for the parameters are constructed. Numerical example is presented in the methods proposed in this paper.
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spelling doaj-art-a0adda57891445259b67d876fcbcdb372025-08-20T03:19:50ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/539860539860Estimation of the Parameters of the Reversed Generalized Logistic Distribution with Progressive Censoring DataZ. A. Abo-Eleneen0E. M. Nigm1Faculty of Computers and Informatics, Zagazig University, Zagazig 44519, EgyptFaculty of Science, Zagazig University, Zagazig 44519, EgyptThe reversed generalized logistic (RGL) distributions are very useful classes of densities as they posses a wide range of indices of skewness and kurtosis. This paper considers the estimation problem for the parameters of the RGL distribution based on progressive Type II censoring. The maximum likelihood method for RGL distribution yields equations that have to be solved numerically, even when the complete sample is available. By approximating the likelihood equations, we obtain explicit estimators which are in approximation to the MLEs. Using these approximate estimators as starting values, we obtain the MLEs using iterative method. We examine numerically MLEs estimators and the approximate estimators and show that the approximation provides estimators that are almost as efficient as MLEs. Also we show that the value of the MLEs decreases as the value of the shape parameter increases. An exact confidence interval and an exact joint confidence region for the parameters are constructed. Numerical example is presented in the methods proposed in this paper.http://dx.doi.org/10.1155/2010/539860
spellingShingle Z. A. Abo-Eleneen
E. M. Nigm
Estimation of the Parameters of the Reversed Generalized Logistic Distribution with Progressive Censoring Data
International Journal of Mathematics and Mathematical Sciences
title Estimation of the Parameters of the Reversed Generalized Logistic Distribution with Progressive Censoring Data
title_full Estimation of the Parameters of the Reversed Generalized Logistic Distribution with Progressive Censoring Data
title_fullStr Estimation of the Parameters of the Reversed Generalized Logistic Distribution with Progressive Censoring Data
title_full_unstemmed Estimation of the Parameters of the Reversed Generalized Logistic Distribution with Progressive Censoring Data
title_short Estimation of the Parameters of the Reversed Generalized Logistic Distribution with Progressive Censoring Data
title_sort estimation of the parameters of the reversed generalized logistic distribution with progressive censoring data
url http://dx.doi.org/10.1155/2010/539860
work_keys_str_mv AT zaaboeleneen estimationoftheparametersofthereversedgeneralizedlogisticdistributionwithprogressivecensoringdata
AT emnigm estimationoftheparametersofthereversedgeneralizedlogisticdistributionwithprogressivecensoringdata