Survival analysis for a new compounded bivariate failure time distribution in shock and competing risk models via an EM algorithm

References

• Aarset, M. V. 1987. How to identify a bathtub hazard rate. IEEE Transactions on Reliability 36:106–8. doi: 10.1109/TR.1987.5222310.
   Web of Science ®Google Scholar
• Adamidis, K., and S. Loukas. 1998. A lifetime distribution with decreasing failure rate. Statistics & Probability Letters 39:35–42. doi: 10.1016/S0167-7152(98)00012-1.
   Web of Science ®Google Scholar
• Al-Khedhairi, A., and A. El-Gohary. 2008. A new class of bivariate gompertz distributions and its mixture. International Journal of Mathematical Analysis 2:235–53.
   Google Scholar
• Bagheri, S. F., E. Bahrami Samani, and M. Ganjali. 2016. The generalized modified weibull power series distribution: Theory and applications. Computational Statistics and Data Analysis 94:136–60. doi: 10.1016/j.csda.2015.08.008.
   Web of Science ®Google Scholar
• Barlow, R. E., and F. Proschan. 1975. Statistical theory of reliability and life testing. New York: Holt, Rinehart and Winston.
   Google Scholar
• Barreto-Souza, W. 2012. Bivariate gamma-geometric law and its induce levy process. Journal of Multivariate Analysis 109:130–45. doi: 10.1016/j.jmva.2012.03.004.
   Web of Science ®Google Scholar
• Barreto-Souza, W., A. L. de Morais, and G. M. Cordeiro. 2011. The weibull-geometric distribution. Journal of Statistical Computation and Simulation 81 (5):645–57. doi: 10.1080/00949650903436554.
   Web of Science ®Google Scholar
• Bowers, N. L., H. U. Gerber, J. C. Hickman, D. A. Jones, and C. J. Nesbitt. 1997. Actuarial mathematics.Schaumburg, IL: Society of Actuaries, second edition,
   Google Scholar
• Carriere, J. F. 2000. Bivariate survival models for coupled lives. Scandinavian Actuarial Journal 2000 (1):17–32. doi: 10.1080/034612300750066700.
   Google Scholar
• Chahkandi, M., and M. Ganjali. 2009. On some lifetime distributions with decreasing failure rate. Computational Statistics and Data Analysis 53 (12):4433–40. doi: 10.1016/j.csda.2009.06.016.
   Web of Science ®Google Scholar
• Dinse, G. 1982. Non-parametric estimation of partially incomplete time and types of failure data. Biometrics 38 (2):417–31.
   PubMedGoogle Scholar
• Frees, E. W., J. Carriere, and E. Valdez. 1996. Annuity valuation with dependent mortality. The Journal of Risk and Insurance 63 (2):229–61. doi: 10.2307/253744.
   Web of Science ®Google Scholar
• Ghitany, M., E. Al-Hussaini, and R. Al-Jarallah. 2005. Marshall-olkin extended weibull distribution and its application to censored data. Journal of Applied Statistics 32 (10):1025–34. doi: 10.1080/02664760500165008.
   Web of Science ®Google Scholar
• Ghitany, M., F. Al-Awadhi, and L. Alkhalfan. 2007. Marshall–olkin extended lomax distribution and its application to censored data. Communications in Statistics-Theory and Methods 36 (10):1855–66. doi: 10.1080/03610920601126571.
   Web of Science ®Google Scholar
• Giesecke, K. 2003. A simple exponential model for dependent defaults. The Journal of Fixed Income 13 (3):74–83. doi: 10.3905/jfi.2003.319362.
   Google Scholar
• Hassan, A. S., and M. Abd-Allah. 2017. Exponentiated lomax geometric distribution: Properties and applications. Pakistan Journal of Statistics and Operation Research 13 (3):545–66. doi: 10.18187/pjsor.v13i3.1437.
   Web of Science ®Google Scholar
• Iyer, S. K., and D. Manjunath. 2004. Correlated bivariate sequences for queueing and reliability applications. Communications in Statistics-Theory and Methods 33 (2):331–50. doi: 10.1081/STA-120028377.
   Web of Science ®Google Scholar
• Jagger, C., and C. J. Sutton. 1991. Death after marital bereavement is the risk increased? Statistics in Medicine 10 (3):395–404.
   PubMed Web of Science ®Google Scholar
• Johnson, N. L., and S. Kotz. 1975. A vector of multivariate hazard rate. Journal of Multivariate Analysis 5 (1):53–66. doi: 10.1016/0047-259X(75)90055-X.
   Google Scholar
• Johnson, R. A., and D. W. Wiechern. 1992. Applied multivariate statistical analysis. New Jersey: Prentice Hall.
   Google Scholar
• Kotz, S., N. Balakrishnan, and N. L. Johnson. 2000. Continuous multivariate distributions. New York: John Wiley and Sons.
   Google Scholar
• Kundu, D. 2004. Parameter estimation for partially complete time and type of failure data. Biometrical Journal 46 (2):165–79. doi: 10.1002/bimj.200210014.
   Web of Science ®Google Scholar
• Kundu, D. 2015. Bivariate geometric generalized exponential distribution. Journal of Data Science 13:693–712.
   Google Scholar
• Kundu, D., and A. Dey. 2009. Estimating the parameters of the marshall-olkin bivariate weibull distribution by em algorithm. Computational Statistics and Data Analysis 35:956–65. doi: 10.1016/j.csda.2008.11.009.
   Google Scholar
• Kundu, D., and A. K. Gupta. 2014. On bivariate weibull-geometric distribution. Journal of Multivariate Analysis 123:19–29. doi: 10.1016/j.jmva.2013.08.004.
   Web of Science ®Google Scholar
• Kundu, D., and R. D. Gupta. 2006. Estimation of r=p(y<x) for weibull distribution. IEEE Transactions on Reliability 55:270–80. doi: 10.1109/TR.2006.874918.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Kundu, D., and R. D. Gupta. 2010. Modified sarhan-balakrishnan singular bivariate distribution. Journal of Statistical Planning and Inference 140 (2):526–38. doi: 10.1016/j.jspi.2009.07.026.
   Web of Science ®Google Scholar
• Lehmann, E. L. 1966. Some concepts of dependence. The Annals of Mathematical Statistics 37 (5):1137–53. doi: 10.1214/aoms/1177699260.
   Google Scholar
• Lindskog, F., and A. J. McNeil. 2003. Common poisson shock models: applications to insurance and credit risk modelling. ASTIN Bulletin 33 (02):209–38. doi: 10.2143/AST.33.2.503691.
   Google Scholar
• Louis, T. A. 1982. Finding the observed information matrix when using the em algorithm. Journal of the Royal Statistical Society 44:226–33. doi: 10.1111/j.2517-6161.1982.tb01203.x.
   Google Scholar
• Louzada, F., V. A. A. Marchi, and M. Roman. 2014. The exponentiated exponential-geometric distribution: a distribution with decreasing, increasing and unimodal failure rate. Statistics 48 (1):167–81. doi: 10.1080/02331888.2012.667103.
   Web of Science ®Google Scholar
• Marshall, A. W., and I. Olkin. 1967. A multivariate exponential distribution. Journal of the American Statistical Association 62 (317):30–44. doi: 10.2307/2282907.
   Web of Science ®Google Scholar
• Marshall, A. W., and I. Olkin. 1988. Families of multivariate distributions. Journal of the American Statistical Association 83 (403):834–41. doi: 10.2307/2289314.
   Web of Science ®Google Scholar
• Marshall, A. W., and I. Olkin. 1997. A new method of adding a parameter to a family of distributions with application to the exponential and weibull families. Biometrika 84 (3):641–52. doi: 10.1093/biomet/84.3.641.
   Web of Science ®Google Scholar
• McLachlan, G. J., and K. Krishnan. 1996. The EM algorithm and extension. New York: Wiley.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• Pham, H., and C. D. Lai. 2007. On recent generalizations of the weibull distribution. IEEE Transactions on Reliability 56 (3):454–8. doi: 10.1109/TR.2007.903352.
   Web of Science ®Google Scholar
• Sankaran, P. G., and D. Kundu. 2014. On a bivariate pareto model. Statistics, Statistics 48 (2):241–55. doi: 10.1080/02331888.2012.719521.
   Web of Science ®Google Scholar
• Sarhan, A. M., and N. Balakrishnan. 2007. A new class of bivariate distributions and its mixture. Journal of Multivariate Analysis 98 (7):1508–27. doi: 10.1016/j.jmva.2006.07.007.
   Web of Science ®Google Scholar
• 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 and Data Analysis 55 (1):644–54. doi: 10.1016/j.csda.2010.06.006.
   Web of Science ®Google Scholar
• Silva, R. B., M. Bourguignon, C. R. B. Dias, and G. M. Cordeiro. 2013. The compound class of extended weibull power series distributions. Computational Statistics and Data Analysis 58:352–67. doi: 10.1016/j.csda.2012.09.009.
   Web of Science ®Google Scholar