Estimation of the Parameters of the Bivariate Generalized Exponential Distribution using Accelerated Life Testing with Censoring Data
-
2014-08-18 https://doi.org/10.14419/ijasp.v2i2.3078 -
Abstract
In this paper, the estimation for the bivariate generalized exponential (BVGE) distribution under type-I censored with constant stress accelerated life testing (CSALT) are discussed. The scale parameter of the lifetime distribution at constant stress levels is assumed to be an inverse power law function of the stress level. The unknown parameters are estimated by the maximum likelihood approach and their approximate variance-covariance matrix is obtained. Then, the numerical studies are introduced to illustrate the approach study using samples which have been generated from the bivariate generalized exponential distribution.
Keywords: Accelerated life testing, Bivariate generalized exponential distribution, Constant stress, Type-I censoring, Maximum likelihood estimation.
-
References
- A. A. Abdel-Ghaly, A. F. Attia and H. M. Aly, "Estimation of The Parameters of Pareto Distribution and The Reliability Function Using Accelerated Life Testing with Censoring", Communications in Statistics Simulation and Computation, 27, (1998), 469-484.
- D. K. Al-MAutrairi, M. E. Gitany and D. Kundu, "A New Bivariate Distribution with Weighted Exponential Marginals and its Multivariate Generalization", Statistical Papers, 52 (4), (2011), 921-936.
- S. K. Ashour, A. A. Essam and H. Z. Muhammed, "Moment Generating Function of The Bivariate Generalized Exponential Distribution", Applied Mathematical Sciences, 3(59), (2009), 2911 – 2918.
- S. K. Ashour, A. A. Essam and H. Z. Muhammed, "Maximum Likelihood Estimation for The Baivariate Generalized Exponential Distribution Parameters using Type I Censored Data", Journal of Applied Sciences Research, 8(4), (2012), 1893-1900.
- A. F. Attia, H. M. Aly and S. O. Bleed, "Estimating and Planning Accelerated Life Test using Constant Stress for Generalized Logistic Distribution under Type-I Censoring", ISRN Applied Mathematics, 203618, (2011), 15 pages.
- A. F. Attia, H. M. Aly and H. Z. Muhammed, "Estimation of the Bivariate Generalized Linear Failure Rate Distribution under Different Censoring Schemes", Proceedings of the 〖47〗^thAnnual Conference in Statistics, Computer Science, and Operations Research, Institute of Statistical Studies and Research, Cairo University, (2013).
- E. A. Elsayed, "Reliability Engineering", Addison Wesley longman, Inc, (1996).
- D. D. Hanagel, "Some Inference Results in Bivariate Exponential Distribution Based on Censored Samples", Communications in Statistics – Theory and Methods, 21(5), (1992), 1273-1295.
- P. Houggard, B. Harvald and N. V. Holm, "Measuring the Similarities between the Lifetimes of Adult Danish Twins Born Between 1881-1930", Journal of Statistical Society Association, 87, (1992), 17-24.
- D. Kundu and R. D. Gupta, "Bivariate Generalized Exponential Distribution", Journal of Multivariate Analysis, 100 (4), (2009), 581 – 593.
- D. Kundu and R. D. Gupta, "Absolute Continuous Bivariate Generalized Exponential Distribution", Journal of Advances in Statistical Analysis, 95 (2), (2011), 169 – 185.
- D. Kundu and A. K. Gupta, "On Bivariate Weibull-Geometric Distribution", Journal of Multivariate Analysis, 123, (2014), 19-29.
- J. F. Lawless, "Confidence Interval Estimation in the Inverse Power Law Model", Journal of the Royal Statistical Society: Series C, 25(2), (1976), 128–138.
- D. Y. Lin, W. Sun and Z. Ying, "Nonparametric Estimation of the Gap Time Distribution for Serial Events with Censored Data", Biometrikia, 86, (1999), 59-70.
- A. W. Marshall and I. Olikn, "A Multivariate Exponential Distribution", Journal of the American Statistical Association, 62, (1967), 30-44.
- W. Nelson, "Accelerated Testing: Statistical Models, Test Plans, and Data Analyses", New Yourk, John Wiley & Sons, (1990).
- S. Shoaee and E. Khorram, "A New Absolute Continuous Bivariate Generalized Exponential Distribution", Statistical Planning and Inference, 142(7), (2012), 2203–2220.
- N. D. Singpurwalla, "A Problem in Accelerated Life Testing", Journal of American Statistical Association, 66, (2012), 841-845.
-
Downloads
-
Received date: 2014-06-25
Accepted date: 2014-07-26
Published date: 2014-08-18