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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

New Bivariate Exponentiated Modified Weibull Distribution

Abdelfattah Mustafa1 and Mohamed A.W. Mahmoud2
  • 1 Mansoura University, Egypt
  • 2 Al-Azhar University, Egypt

Abstract

The new modified Weibull distribution named exponentiated modified Weibull distribution introduced by many authors. In this study, we define and study a bivariate modified Weibull distribution. Some joint probability functions and conditional probability density function are obtained. Also, joint survival function is expressed in compact form. Several statistical properties of this distribution are discussed. In the area of stress-strength models, we estimate the reliability follow a bivariate exponentiated modified Weibull distribution with dependence between stress and strength variables. Parameters estimators using the maximum likelihood method are obtained. Moreover, a numerical illustration is used to obtain Maximum Likelihood Estimators (MLEs).

Journal of Mathematics and Statistics
Volume 13 No. 4, 2017, 330-338

DOI: https://doi.org/10.3844/jmssp.2017.330.338

Submitted On: 5 August 2017 Published On: 31 October 2017

How to Cite: Mustafa, A. & Mahmoud, M. A. (2017). New Bivariate Exponentiated Modified Weibull Distribution. Journal of Mathematics and Statistics, 13(4), 330-338. https://doi.org/10.3844/jmssp.2017.330.338

Open AccessCopyright: © 2017 Abdelfattah Mustafa and Mohamed A.W. Mahmoud. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Generalized Modified Weibull Distribution
  • Maximum Likelihood Estimators
  • Bivariate Distributions
  • Stress-Strength Models