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Bivariate generalized exponential distribution

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  • Kundu, Debasis
  • Gupta, Rameshwar D.

Abstract

Recently it has been observed that the generalized exponential distribution can be used quite effectively to analyze lifetime data in one dimension. The main aim of this paper is to define a bivariate generalized exponential distribution so that the marginals have generalized exponential distributions. It is observed that the joint probability density function, the joint cumulative distribution function and the joint survival distribution function can be expressed in compact forms. Several properties of this distribution have been discussed. We suggest to use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters and also obtain the observed and expected Fisher information matrices. One data set has been re-analyzed and it is observed that the bivariate generalized exponential distribution provides a better fit than the bivariate exponential distribution.

Suggested Citation

  • Kundu, Debasis & Gupta, Rameshwar D., 2009. "Bivariate generalized exponential distribution," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 581-593, April.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:4:p:581-593
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    References listed on IDEAS

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    1. Sarhan, Ammar M. & Balakrishnan, N., 2007. "A new class of bivariate distributions and its mixture," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1508-1527, August.
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    Cited by:

    1. Kundu, Debasis & Franco, Manuel & Vivo, Juana-Maria, 2014. "Multivariate distributions with proportional reversed hazard marginals," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 98-112.
    2. Manuel Franco & Juana-María Vivo & Debasis Kundu, 2020. "A Generator of Bivariate Distributions: Properties, Estimation, and Applications," Mathematics, MDPI, vol. 8(10), pages 1-30, October.
    3. Ji Hwan Cha & Massimiliano Giorgio, 2018. "Modelling of Marginally Regular Bivariate Counting Process and its Application to Shock Model," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1137-1154, December.
    4. Fatih Kızılaslan & Mustafa Nadar, 2018. "Estimation of reliability in a multicomponent stress–strength model based on a bivariate Kumaraswamy distribution," Statistical Papers, Springer, vol. 59(1), pages 307-340, March.
    5. Saralees Nadarajah, 2011. "The exponentiated exponential distribution: a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(3), pages 219-251, September.
    6. Sarhan, Ammar M. & Hamilton, David C. & Smith, Bruce & Kundu, Debasis, 2011. "The bivariate generalized linear failure rate distribution and its multivariate extension," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 644-654, January.
    7. Wang, Liang & Tripathi, Yogesh Mani & Dey, Sanku & Zhang, Chunfang & Wu, Ke, 2022. "Analysis of dependent left-truncated and right-censored competing risks data with partially observed failure causes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 285-307.
    8. Kundu, Debasis & Gupta, Arjun K., 2014. "On bivariate Weibull-Geometric distribution," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 19-29.
    9. Debasis Kundu, 2021. "Stationary GE-Process and its Application in Analyzing Gold Price Data," Papers 2201.02568, arXiv.org.
    10. Debasis Kundu, 2022. "Bivariate Semi-parametric Singular Family of Distributions and its Applications," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 846-872, November.
    11. Guan, Qiang & Tang, Yincai & Xu, Ancha, 2013. "Objective Bayesian analysis for bivariate Marshall–Olkin exponential distribution," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 299-313.
    12. Vilca, Filidor & Romeiro, Renata G. & Balakrishnan, N., 2016. "A bivariate Birnbaum–Saunders regression model," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 169-183.
    13. Muhammad Mohsin & Hannes Kazianka & Jürgen Pilz & Albrecht Gebhardt, 2014. "A new bivariate exponential distribution for modeling moderately negative dependence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(1), pages 123-148, March.
    14. Calabrese, Raffaella & Osmetti, Silvia Angela, 2019. "A new approach to measure systemic risk: A bivariate copula model for dependent censored data," European Journal of Operational Research, Elsevier, vol. 279(3), pages 1053-1064.
    15. Li, Yang & Sun, Jianguo & Song, Shuguang, 2012. "Statistical analysis of bivariate failure time data with Marshall–Olkin Weibull models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2041-2050.
    16. M. S. Eliwa & M. El-Morshedy, 2019. "Bivariate Gumbel-G Family of Distributions: Statistical Properties, Bayesian and Non-Bayesian Estimation with Application," Annals of Data Science, Springer, vol. 6(1), pages 39-60, March.
    17. Muhammed, Hiba Z., 2020. "On a bivariate generalized inverted Kumaraswamy distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    18. Mercier, Sophie & Pham, Hai Ha, 2017. "A bivariate failure time model with random shocks and mixed effects," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 33-51.
    19. Denys Pommeret, 2013. "A two-sample test when data are contaminated," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 501-516, November.
    20. Debasis Kundu, 2022. "Stationary GE-Process and its Application in Analyzing Gold Price Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 575-595, November.
    21. Ali Genç, 2014. "Distribution of product and quotient of bivariate generalized exponential distribution," Statistical Papers, Springer, vol. 55(3), pages 785-803, August.
    22. S. Mirhosseini & M. Amini & D. Kundu & A. Dolati, 2015. "On a new absolutely continuous bivariate generalized exponential distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 61-83, March.

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