438
Views
8
CrossRef citations to date
0
Altmetric
Articles

An extended Gompertz-Makeham distribution with application to lifetime data

Pages 2454-2475 | Received 20 Jan 2017, Accepted 26 Jun 2017, Published online: 31 Jul 2017

References

  • Aarset, M. V. (1987). How to identify bathtub hazard rate. IEEE Transactions on Reliability R-36:106–08.
  • Abdul-Moniem, I. B. (2015). Transmuted Burr type III distribution. Journal of Statistics: Advances in Theory and Applications 14:37–47.
  • Abdul-Moniem, I. B., and Seham, M. (2015). Transmuted Gompertz distribution. Computational and Applied Mathematics Journal 3:88–96.
  • Bailey, R. C., Homer, L. D., and Summe, J. P. (1977). A proposal for the analysis of kidney graft survival. Transplantation 24:309–15.
  • Bailey, R. C. (1978). Limiting forms of the Makeham model and their use for survival analysis of transplant studies. Biometrics 34:725–25.
  • Bemmaor, A. C. (1994). Modeling the diffusion of new durable goods: Word-of-mouth effect versus consumer heterogeneity. Research Traditions in Marketing, G. Laurent, G. L. Lilien, B.Pras, (eds.). Int. Ser. In Quantitative Marketing 5, Kluwer, Boston, pp. 201–23.
  • Gail, M. H. (2009). Applying the Lorenz curve to disease risk to optimize health benefits under cost constraints. Statistics and Its Interface 2:117–21. MR2516062
  • Chukwu, A. U., and Ogunde, A. A. (2016). On Kumaraswamy Gompertz Makeham distribution. American Journal of Mathematics and Statistics 6:122–27.
  • Gupta, R. D., and Kundu, D. (2009). A new class of weighted exponential distribution. Statistics 43:621–34.
  • Groves-Kirkby, C. J., Denman, A. R., and Phillips, P. S. (2009). Lorenz curve and Gini coefficient: Novel tools for analyzing seasonal variation of environmental radon gas. Journal of Environmental Management 90:2480–87.
  • Elbatel, I., and Aryal, G. (2013). On the transmuted additive Weibull distribution. Austrian Journal of Statistics 42:117–32.
  • Elbatel, I., Diab, L. S., and Abdul Alim, N. A. (2013). Transmuted generalized linear exponential distribution. International Journal of Computer Applications 83:29–37.
  • Galton, F. (1883). Enquiries onto human faculty and its development. London: Macmillan & Company.
  • Gupta, R. C., and Kirmani, S. N. U. A. (2000). Residual coefficient of variation and some characterization results. Journal of Statistical Planning and Inference 91:23–31.
  • Izadkhan, S., and Kayid, M. (2013). Reliability analysis of the harmonic mean inactivity time order. IEEE Transactions on Reliability 62:329–37.
  • Jodrá, P. (2009). A closed-form expression for the quantile function of the Gompertz - Makeham distribution. Mathematics and Computers in Simulation 79:3069–75.
  • Jodrá, P. (2010). Computer generation of random variables with Lindley or Poisson-Lindley distribution via the Lambert W function. Mathematics and Computers in Simulation 81:851–59.
  • Kayid, M., and Ahmad, I. A. (2004). On the mean inactivity time ordering with reliability applications. Probability in the Engineering and Informational Sciences 18:395–09.
  • Kayid, M., and Izadkhah, S. (2014). Mean inactivity time function, associated orderings and classes of life distribution. IEEE Transactions on Reliability 63:593–602.
  • Khan, M. S., King, R. (2013). Transmuted modified Weibull distribution: A generalization of the modified Weibull probability distribution. European Journal of Pure and Applied Mathematics 6:66--88.
  • Kleiber, C., and Kotz, S. (2003). Statistical size distribution in economics and actuarial sciences. Ney York: Wiley. MR1994050.
  • Makeham, W. M. (1860). On the law of mortality and construction of annuity tables. Journal of the Institute of Actuaries and Assurance Magazine 8:301–10.
  • Merovci, F. (2013a). Transmuted exponentiated exponential distribution. Mathematical Sciences and Applications E-Notes 1:112–22.
  • Merovci, F. (2013b). Transmuted Lindley distribution. International Journal of Open Problems in Computer Science and Mathematics 6:63–72.
  • Missov, T. I., and Lenart, A. (2013). Gompertz-Makeham life expectancies: Expressions and applications. Theoretical Population Biology 90:39–35.
  • Moors, J. J. (1988). A quantile alternative for kurtosis. Journal of the Royal Statistical Society D 37:25–32.
  • Pundir, S., Arora, S., and Jain, K. (2005). Bonferroni curve and the related statistical inference. Statistics and Probability Letters 75:140–50.
  • Radice, A. (2009). Use of the Lorenz curve to quantify statistical nonuniformity of sediment transport rate. Journal of Hydraulic Engineering 135:320–26.
  • Shaked, M., and Shanthikumar, J. G. (1994). Stochastic orders and their applications. New York: Academic Press.
  • Shaw, W. T., and Buckley, I. R. (2009). The alchemy of probability distribution: beyond Gram- Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. Technical report, http://arxiv.org/abs/0901.0434.
  • Teimouri, M., and Gupta, A. K. (2012). Estimation methods for the Gompertz-Makeham distribution under progressively type-I interval censoring scheme. National Academy Science Letters 35:227–35.
  • Wrycza, T. F. (2014). Entropy of the Gompertz-Makeham mortality model. Demographic Research 30:1397–404.
  • Zagrafos, K., and Balakrishnan, N. (2009). On families of beta-and generalized gamma-generated distributions and associated inference. Statistical Methodology 6:344–62.

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.