A Proportional Hazard Marshall–Olkin Extended Family of Distributions and its Application to Gompertz Distribution

References

• Arnold, B.C., Balakrishnan, N., Nagaraja, H.N. (1992). A First Course in Order Statistics. New York: Wiley.
   Google Scholar
• Barlow, R.E., Proschan, F. (1975). Statistical Theory of Reliability and Life Testing: Probability Models. New York: Holt, Rinehart, and Winston.
   Google Scholar
• Garg, M.L., Rao, B.R., Redmond, C.K. (1970). Maximum likelihood estimation of the parameters of the Gompertz survival function. J. Royal Stat. Society C 19: 152–159.
   Web of Science ®Google Scholar
• Ghitany, M.E. (2005). Marshall-Olkin extended Pareto distribution and its application. Int. J. Appl. Math. 18: 17–31.
   Google Scholar
• Ghitany, M.E., AL-Hussaini, E.K., Al-Jarallah, R.A. (2005). Marshall-Olkin extended Weibull distribution and its application to censored data. J. Appl. Stat. 32: 1025–1034.
   Web of Science ®Google Scholar
• Ghitany, M.E., AL-Awadhi, F.A., Alkhalfan, L.A. (2007a). Marshall-Olkin extended Lomax distribution and its application to censored data. Commun. Stat.-Theor. Methods 36: 1855–1866.
   Web of Science ®Google Scholar
• Ghitany, M.E., Kotz, S. (2007b). Reliability properties of extended linear failure-rate distributions. Probab. Eng. Inf. Sci. 21: 441–450.
   Web of Science ®Google Scholar
• Gompertz, B. (1825). On the nature of the function expressive on the law of human mortality. Philosophical Trans. Royal Society London 115: 513–583.
   Google Scholar
• Gupta, R.C., Peng, C. (2009). Estimation of reliability in proportional odds ratio models. Comput. Stat. Data Anal. 53: 01495–1510.
   Web of Science ®Google Scholar
• Gupta, R.C., Lvin, S., Peng, C. (2010). Estimating turning points of the failure rate of the extended Weibull distribution. Comput. Stat. Data Anal. 54: 924–934.
   Web of Science ®Google Scholar
• Jayakumar, K., Mathew, T. (2008). On a generalization to Marshall-Olkin scheme and its application to Burr type XII distribution. Stat. Papers 49: 421–439.
   Web of Science ®Google Scholar
• Jose, K.K., Naik, S.R., Ristić, M.M. (2010). Marshall-Olkin q-Weibull distribution and max-min processes. Stat. Papers 51: 837–851.
   Web of Science ®Google Scholar
• Kaplan, E.L., Meier, P. (1958). Nonparametric estimation from incomplete observations. J. Am. Stat. Assoc. 53: 457–481.
   Web of Science ®Google Scholar
• Kunimura, D. (1998). The Gompertz distribution—estimation of parameters. Actuarial Res. Clearing House 2: 65–76.
   Google Scholar
• Marshall, A.W., Olkin, I. (1997). A new method for adding a parameter to a family of distributions with applications to the exponential and Weibull families. Biometrika 84: 641–652.
   Web of Science ®Google Scholar
• Marshall, A.W., Olkin, I. (2007). Life Distributions: Structure of Nonparametric, Semiparametric, and Parametric Families. New York: Springer.
   Google Scholar
• Miller, P.G. Jr (1981). Survival Analysis. New York: Wiley.
   Google Scholar
• Missov, T.I., Lenart, A. (2011). Linking period and cohort life-expectancy linear increases in Gompertz proportional hazards models. Demographic Res. 24(19): 455–468.
   Web of Science ®Google Scholar
• Pollard, J.H., Valkovics, E.J. (1992). The Gompertz distribution and its applications. Genus 48(3-4): 15–28.
   PubMedGoogle Scholar
• Sankaran, P.G., Jayakumar, K. (2008). On proportional odds models, Stat. Papers 49: 779–789.
   Web of Science ®Google Scholar
• Shaked, M., Shanthikumar, J.G. (2007). Stochastic Orders. New York: Springer.
   Google Scholar
• Silva, A.N.F. (2004). Estudo evolutivo das crianças expostas ao HIV e notificadas pelo núcleo de vigilância epidemiológica do HCFMRP-USP. M.Sc. Thesis. University of São Paulo, Brazil.
   Google Scholar
• Wetterstrand, W.H. (1981). Parametric models for life insurance mortality data: Gompertz’s law over time. Trans. Society Actuaries 33: 159–175.
   Google Scholar
• Witten, M., Satzer, W. (1992). Gompertz survival model parameters: estimation and sensitivity. Appl. Math. Letters 5(1): 7–12.
   Web of Science ®Google Scholar
• Wu, J-W, Hung, W-L, Tsai, C-H (2004). Estimation of parameters of the Gompertz distribution using the least squares method. Appl. Math. Comput. 158: 133–147.
   Web of Science ®Google Scholar