The exponentiated transmuted Weibull geometric distribution with application in survival analysis

ABSTRACT

This article introduces a new generalization of the transmuted Weibull distribution introduced by Aryal and Tsokos in 2011. We refer to the new distribution as exponentiated transmuted Weibull geometric (ETWG) distribution. The new model contains 22 lifetime distributions as special cases such as the exponentiated Weibull geometric, complementary Weibull geometric, exponentiated transmuted Weibull, exponentiated Weibull, and Weibull distributions, among others. The properties of the new model are discussed and the maximum likelihood estimation is used to evaluate the parameters. Explicit expressions are derived for the moments and examine the order statistics. To examine the performance of our new model in fitting several data we use two real sets of data, censored and uncensored, and then compare the fitting of the new model with some nested and nonnested models, which provides the best fit to all of the data. A simulation has been performed to assess the behavior of the maximum likelihood estimates of the parameters under the finite samples. This model is capable of modeling various shapes of aging and failure criteria.

KEYWORDS:

• Entropies
• Inversion method
• Maximum likelihood estimation
• Moment generating function
• Order statistics
• Reliability function
• Transmutation

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 33C90
• 62E99

Acknowledgments

The authors are grateful to the reviewers and the Editorial Board for their valuable comments that have improved the original version of the article. This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah. The authors, therefore, acknowledge with thanks DSR technical and financial support.