International journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN:2313-626X

Frequency: 12
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 Volume 5, Issue 12 (December 2018), Pages: 100-111

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 Original Research Paper

 Title: A new family based on lifetime distribution: Bivariate Weibull-G models based on Gaussian copula

 Author(s): Zakiah Ibrahim Kalantan 1, *, Mervat Khalifah Abd Elaal 1, 2

 Affiliation(s):

 1Department of Statistics, King Abdulaziz University, Jeddah, Saudi Arabia
 2Department of Statistics, Al-Azhar University, Cairo, Egypt

 https://doi.org/10.21833/ijaas.2018.12.012

 Full Text - PDF          XML

 Abstract:

Copula method plays an essential rule to study the dependence between data variables especially in bivariate distribution. It is noted that some bivariate models are constructed with uncomplete information of distributions. Copula improves the reliability of applications such as flood peak. Weibull distribution is a popular used in engineering, theory, medical and survival analysis. Despite its spread, it is known that the Weibull distribution could not implement the data set with non-monotone failure rate. In such case, many papers have suggested a modification and generalization of Weibull model. One of generalization is made through the baseline distribution by adding more shape parameters. The main purpose of our paper is to present some new bivariate Weibull models with respect to G cumulative distributions of baseline distribution. This approach converges the power series of probability distribution.  We use the copula function to construct the bivariate Weibull distribution. The proposed models provide high flexibility and can be used effectively for modeling dataset with a different structure. We provide special cases in details namely; bivariate Weibull-exponential, bivariate Weibull-Rayleigh and bivariate Weibull Chi-square. We use Gaussian copula function to merge the dependent distributions, this copula is popular used in various applications like econometrics and finance. We discuss some structural properties of the proposed models. In order to estimate the model parameters, we discuss parametric methods via maximum likelihood estimation and modified maximum likelihood methods. In addition, we use the moment methods as semi-parametric methods for parameters estimations. Finally, Simulations are studied to illustrate methods of inference discussed and study the performance of new distributions. 

 © 2018 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Weibull-G distributions, Bivariate Weibull-G distributions, Maximum likelihood method, Copula, Parametric/semi-parametric methods

 Article History: Received 12 July 2018, Received in revised form 6 October 2018, Accepted 14 October 2018

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2018.12.012

 Citation:

 Kalantan ZI and Elaal MKA (2018). A new family based on lifetime distribution: Bivariate Weibull-G models based on Gaussian copula. International Journal of Advanced and Applied Sciences, 5(12): 100-111

 Permanent Link:

 http://www.science-gate.com/IJAAS/2018/V5I12/Kalantan.html

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