336
Views
6
CrossRef citations to date
0
Altmetric
Articles

A bivariate inverse generalized exponential distribution and its applications in dependent competing risks model

&
Pages 7019-7036 | Received 23 Jan 2020, Accepted 05 Sep 2020, Published online: 28 Sep 2020

References

  • Al-Hussaini, E. K., and M. Ahsanullah. 2015. Exponentiated distributions. Paris, France: Atlantis Press.
  • Arnold, B. C. 1968. Parameter estimation for a multivariate exponential distribution. Journal of the American Statistical Association 63:848–52.
  • Barreto-Souza, W., and A. J. Lemonte. 2013. Bivariate Kumaraswamy distribution: Properties and a new method to generate bivariate classes. Statistics 47 (6):1321–42. doi:10.1080/02331888.2012.694446.
  • Baxter, L. A., and S. T. Rachev. 1991. The stability of a characterization of the bivariate Marshall-Olkin distribution. Journal of Mathematical Analysis and Applications 160 (2):563–73. doi:10.1016/0022-247X(91)90326-U.
  • Begum, A. A., and A. H. Khan. 2000. Concomitants of order statistics from Marshall and Olkin’s bivariate Weibull distribution. Calcutta Statistical Association Bulletin 50 (1–2):65–198. doi:10.1177/0008068320000106.
  • Bemis, B., L. J. Bain, and J. J. Higgins. 1972. Estimation and hypothesis testing for the parameters of a bivariate exponential distribution. Journal of the American Statistical Association 67 (340):927–29. doi:10.1080/01621459.1972.10481320.
  • Boland, P. J. 1998. An arrangement increasing property of the Marshall-Olkin bivariate exponential. Statistics & Probability Letters 37 (2):167–70. doi:10.1016/S0167-7152(97)00114-4.
  • Cai, J., Y. Shi, and B. Liu. 2017. Analysis of incomplete data in the presence of dependent competing risks from Marshall-Olkin bivariate Weibull distribution under progressive hybrid censoring. Communications in Statistics - Theory and Methods 46 (13):6497–511. doi:10.1080/03610926.2015.1129420.
  • Cox, D. R. 1959. The analysis of exponentially distributed lifetimes with two types of failures. Journal of the Royal Statistical Society, Series B 21:411–21.
  • Crowder, M. J. 2011. Classical competing risks. Boca Raton, FL: Chapman & Hall.
  • D’Agostino, R. B., and M. A. Stephens. 1986. Goodness-of-fit techniques. New York: Marcel and Dekker.
  • Feizjavadian, S. H., and R. Hashemi. 2015. Analysis of dependent competing risks in presence of progressive hybrid censoring using Marshall-Olkin bivariate Weibull distribution. Computational Statistics & Data Analysis 82:19–34. doi:10.1016/j.csda.2014.08.002.
  • Gupta, R. C., S. N. U. A. Kirmani, and N. Balakrishnan. 2013. On a class of generalized Marshall-Olkin bivariate distributions and some reliability characteristics. Probability in the Engineering and Informational Sciences 27 (2):261–75. doi:10.1017/S0269964813000107.
  • Gupta, R. D., and D. Kundu. 1999. Generalized exponential distribution. Australian & New Zealand Journal of Statistics 41 (2):173–88. doi:10.1111/1467-842X.00072.
  • Kundu, D., and A. K. Dey. 2009. Estimating the parameters of the Marshall Olkin bivariate Weibull distribution by EM algorithm. Computational Statistics & Data Analysis 53 (4):956–65. doi:10.1016/j.csda.2008.11.009.
  • Kundu, D., and A. Gupta. 2017. On bivariate inverse Weibull distribution. Brazilian Journal of Probability and Statistics 31 (2):275–302. doi:10.1214/16-BJPS313.
  • Kundu, D., and A. K. Gupta. 2013. Bayes estimation for the Marshall-Olkin bivariate Weibull distribution. Computational Statistics & Data Analysis 57 (1):271–81. doi:10.1016/j.csda.2012.06.002.
  • Kundu, D., and R. D. Gupta. 2009. Bivariate generalized exponential distribution. Journal of Multivariate Analysis 100 (4):581–93. doi:10.1016/j.jmva.2008.06.012.
  • Kundu, D., and R. D. Gupta. 2010a. A class of bivariate models with proportional reversed hazard marginals. Sankhya Series B 72 (2):236–53. doi:10.1007/s13571-011-0012-1.
  • Kundu, D., and R. D. Gupta. 2010b. Modified Sarhan-Balakrishnan singular bivariate distribution. Journal of Statistical Planning and Inference 140 (2):526–38. doi:10.1016/j.jspi.2009.07.026.
  • Lai, C.-D., G. D. Lin, K. Govindaraju, and S. A. Pirikahu. 2017. A simulation study on the correlation structure of Marshall-Olkin bivariate Weibull distribution. Journal of Statistical Computation and Simulation 87 (1):156–70. doi:10.1080/00949655.2016.1195832.
  • Louis, T. A. 1982. Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, Series B 44:226–33.
  • Lu, J.-C. 1989. Weibull extension of the Freund and Marshall-Olkin bivariate exponential model. IEEE Transactions on Reliability 38 (5):615–19. doi:10.1109/24.46492.
  • Marshall, A. W., and I. Olkin. 1967. A multivariate exponential distribution. Journal of the American Statistical Association 62 (317):30–44. doi:10.1080/01621459.1967.10482885.
  • Meintanis, S. G. 2007. Test of fit for Marshall-Olkin distributions with applications. Journal of Statistical Planning and Inference 137 (12):3954–63. doi:10.1016/j.jspi.2007.04.013.
  • Nadarajah, S. 2011. The exponentiated exponential distribution; a survey. AStA Advances in Statistical Analysis 95 (3):219–51. doi:10.1007/s10182-011-0154-5.
  • Nelsen, R. B. 2006. An introduction to copulas. 2nd ed. New York: Springer.
  • Oguntunde, P. E., and A. O. Adejumo. 2015. The generalized inverted generalized exponential distribution with an application to a censored Data. Journal of Statistics Applications and Probability 4:223–30.
  • Pena, E. A., and A. K. Gupta. 1990. Bayes estimation for the Marshall-Volkin exponential distribution. Journal of the Royal Statistical Society, Series B 52:379–89.
  • Popović, B. V., M. M. Ristić, and A. I. Genç. 2020. Dependence properties of multivariate distributions with proportional hazard rate marginals. Applied Mathematical Modelling 77:182–98. doi:10.1016/j.apm.2019.07.030.
  • Ristić, M. M., B. V. Popović, K. Zografos, and N. Balakrishnan. 2018. Discrimination among bivariate beta-generated distributions. Statistics 52 (2):303–20. doi:10.1080/02331888.2017.1397156.
  • Sarhan, A. M., and N. Balakrishnan. 2007. A new class of bivariate distribution and its mixture. Journal of Multivariate Analysis 98 (7):1508–27. doi:10.1016/j.jmva.2006.07.007.
  • Sarhan, A. M., D. C. Hamilton, B. Smith, and D. Kundu. 2011. The bivariate generalized linear failure rate distribution and its multivariate extension. Computational Statistics & Data Analysis 55 (1):644–54. doi:10.1016/j.csda.2010.06.006.
  • Shen, Y., and A. Xu. 2018. On the dependent competing risks using Marshall-Olkin bivariate Weibull model: Parameter estimation with different methods. Communications in Statistics - Theory and Methods 47 (22):5558–72. doi:10.1080/03610926.2017.1397170.
  • Srivastava, D. K., and G. S. Mudholkar. 2003. Goodness-of-fit tests for univariate and multivariate normal models. Handbook of statistics, 869–956. Vol. 22. Amsterdam: North-Holland.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.