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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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| 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. |
| format | Article |
| id | doaj-art-a0adda57891445259b67d876fcbcdb37 |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| 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 |