The generalized inverse Lindley distribution: A new inverse statistical model for the study of upside-down bathtub data

References

• Barnham, K., Anderson, D., White, G., Brownie, C., Pullock, K. (1987). Design and Analysis Methods for Fish Survival Analysis based on Release-Recapture. Bethesda, Maryland: American Fisheries Society, Monograph 5.
   Google Scholar
• Bennette, S. (1983). Log-logistic regression models for survival data. Appl. Stat. 32:165–171.
   Web of Science ®Google Scholar
• Calabria, R., Pulcini, G. (1994). Bayesian 2-sample prediction for the inverse Weibull distribution. Commun. Stat. A: Theory Methods 23:1811–1821.
   Web of Science ®Google Scholar
• Chen, Z. (2000). A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Stat. Probab. Lett. 49:155–161.
   Web of Science ®Google Scholar
• Cheng, R., Amin, N. (1981). Maximum likelihood estimation of parameters in the inverse gaussian distribution, with unknown origin. Technometrics 23:257–263.
   Web of Science ®Google Scholar
• Cheng, R., Amin, N. (1983). Estimating parameters in continuous univariate distributions with a shifted origin. J. R. Stat. Soc. Ser. B (Methodol.) 45:394–403.
   Google Scholar
• Cordeiro, G.M., de Castro, M. (2011). A new family of generalized distributions. J. Stat. Comput. Simul. 81:883–898.
   Web of Science ®Google Scholar
• Deshpande, J.V., Suresh, R.P. (1990). Non-monotonic ageing. Scand. J. Stat. 17:257–262.
   Google Scholar
• Dumonceaux, R., Antle, C. (1973). Discrimination between the lognormal and Weibull distribution. Technometrics 15:923–926.
   Web of Science ®Google Scholar
• Efron, B. (1988). Logistic regression, survival analysis, and the Kaplan-Meier curve. J. Am. Stat. Assoc. 83:414–425.
   Web of Science ®Google Scholar
• Erto, P., Rapone, M. (1984). Non-informative and practical Bayesian confidence bounds for reliable life in the Weibull model. Reliab. Eng. 7:181–191.
   Google Scholar
• Folks, J.L., Chhikara, R.S. (1978). The inverse gaussian distribution and its statistical application – a review. J. R. Stat. Soc. Ser. B (Methodol.) 40:263–289.
   Google Scholar
• Ghitany, M., Al-Mutairi, D., Balakrishnan, N., Al-Enezi, L. (2013). Power Lindley distribution and associated inference. Comput. Stat. Data Anal. 64:20–33.
   Web of Science ®Google Scholar
• Ghitany, M., Atieh, B., Nadarajah, S. (2008). Lindley distribution and its application. Math. Comput. Simul. 78:493–506.
   Web of Science ®Google Scholar
• Glaser, R.E. (1980). Bathtub and related failure rate characterizations. Journal of the American Statistical Association 75:667–672.
   Google Scholar
• Glen, A.G. (2011). On the inverse gamma as a survival distribution. J. Qual. Technol. 43:158–166.
   Web of Science ®Google Scholar
• Gompertz, B. (1825). On the nature of the function expressive on the law of human mortality, and on a new mode of determining the value of life contingencies. Philos. Trans. R. Soc. Lond. 115:513–583.
   Google Scholar
• Gupta, R.D., Kundu, D. (2009). Introduction of shape/skewness parameter(s) in a probability distribution. J. Probab. Stat. Sci. 7:153–171.
   Google Scholar
• Jones, M.C. (2004). Families of distributions arising from distributions of order statistics. Sociedad de Estad stica e I vestigacidn Operativa. Test 13:1–43.
   Google Scholar
• Jorda, P. (2010). Computer generation of random variables with Lindley or Poisson–Lindley distribution via the lambert w function. Math. Comput. Simul. 81:851–859.
   Web of Science ®Google Scholar
• Langlands, A., Pocock, S., Kerr, G., Gore, S. (1997). Long-term survival of patients with breast cancer: a study of the curability of the disease. Br. Med. J. 2:1247–1251.
   Web of Science ®Google Scholar
• Lawless, J. (1982). Statistical Models and Methods for Lifetime Data. New York: John Wiley & Sons.
   Google Scholar
• Lindley, D. (1958). Fiducial distributions and Bayes theorem. J. R. Stat. Soc. Ser. B 20:102–107.
   Google Scholar
• Maswadah, M. (2010). Conditional confidence interval estimation for the inverse Weibull distribution based on censored generalized order statistics. J. Stat. Comput. Simul. 73:887–898.
   Web of Science ®Google Scholar
• Mead, M. (2013). Generalized inverse gamma distribution and its application in reliability. Commun. Stat.-Theory Methods. doi:10.1080/03610926.2013.768667.
   Web of Science ®Google Scholar
• Mudholkar, G., Srivastava, D. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Trans. Reliab. 42:299–302.
   Web of Science ®Google Scholar
• Murthy, D.P., Xie, M., Jiang, R. (2004). Weibull Models. Hoboken, New Jersey: John Wiley & Sons.
   Google Scholar
• Nadarajah, S., Bakouch, H., Tahmasbi, R. (2011). A generalized Lindley distribution. Sankhya B 73:331–359.
   Google Scholar
• Nelson, W. (1982). Applied Life Data Analysis. Hoboken, New Jersey: John Wiley & Sons.
   Google Scholar
• R Core Team. (2012). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. ISBN 3-900051-07-0. Available at: http://www.R-project.org/.
   Google Scholar
• Rényi, A. (1961). On measures of entropy and information. In: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, (pp. 547–561). Volume 1, Contributions to the Theory of Statistics, Berkeley, California: University of California Press.
   Google Scholar
• Seshadri, V. (1999). The Inverse Gaussian Distribution. Statistical Theory and Applications. New York: Springer-Verlag.
   Google Scholar
• Shaked, M., Shanthikumar, J. (1994). Stochastic Orders and Their Applications. Boston: Academic Press.
   Google Scholar
• Sharma, V.K., Singh, S.K., Singh, U., Agiwal, V. (2015). The inverse Lindley distribution: A stress-strength reliability model with application to head-and neck cancer data. Journal of Industrial and Production Engineering 32:162–173.
   Google Scholar
• Singh, S.K., Singh, U., Sharma, V.K. (2013a). Bayesian prediction of future observations from inverse Weibull distribution based on Type-II hybrid censored sample. Int. J. Adv. Stat. Probab. 1:32–43.
   Google Scholar
• Singh, S.K., Singh, U., Sharma, V.K. (2013b). Expected total test time and Bayesian estimation for generalized Lindley distribution under progressively Type-II censored sample where removals follow the beta-binomial probability law. Appl. Math. Comput. 222:402–419. doi:10.1016/j.amc.2013.07.058.
   Web of Science ®Google Scholar
• Upadhyay, S., Peshwani, M. (2003). Choice between Weibull and log-normal models: a simulation based Bayesian study. Commun. Stat. Theory Methods 32:381–405.
   Web of Science ®Google Scholar
• Weibull, W. (1951). A statistical distribution of wide applicability. J. Appl. Mech. 18:293–297.
   Web of Science ®Google Scholar
• Xie, M., Goh, T., Tang, Y. (2002). A modified Weibull extension with bathtub-shaped failure rate function. Reliab. Eng. Syst. Saf. 76:279–285.
   Web of Science ®Google Scholar
• Xie, M., Lai, C. (1996). Reliability analysis using an additive Weibull model with bathtub shaped failure rate function. Reliab. Eng. Syst. Saf. 52:87–93.
   Web of Science ®Google Scholar