Existence and estimation of critical negative Gompertz parameter

Computers and Mathematics with Applications

Volumn 55, Issue 8, 2008, Pages 1686-1692

  Lakshminarayanan, E S ^a   Pitchaimani, M ^a  

^a MADURAI KAMARAJ UNIVERSITY   (India)

Author keywords

Demographic models; Gompertz equation; Gompertz parameter; Mortality rates; Negative critical Gompertz parameter; Population modeling; Survival function

Indexed keywords

COMPUTER SIMULATION; DATA PROCESSING; MATHEMATICAL MODELS; PROBLEM SOLVING;

DEMOGRAPHIC MODELS; GOMPERTZ EQUATION; GOMPERTZ PARAMETER; MORTALITY RATES; NEGATIVE CRITICAL GOMPERTZ PARAMETER; POPULATION MODELING; SURVIVAL FUNCTION;

PARAMETER ESTIMATION;

EID: 40649123516     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2007.06.006     Document Type: Article

References (25)

1. Gompertz B. On the nature of the function expressive of the law of human mortality and on a new mode of determining the value of life contingencies. Philos. Trans. R. Soc. 115 (1825) 513-585
2. Finch C.E. Longevity Senescence and the Genome (1990), The University of Chicago Press, Chicago
3. Witten M. A return to time, cells and aging. 5. Further thoughts on Gompertzian survival dynamics: The geriatric years. Mech. Ageing Dev. 46 (1988) 175-200
4. Carey J.R., Liedo P., Orozco D., and Vaupel J.W. Slowing of mortality rates at older ages in large medfly cohorts. Science 258 (1992) 457-461
5. Vaupel J.W. Trajectories of mortality at advanced ages. In: Wacher K.W., and Finch C.E. (Eds). Between Zeus and the Salmon (The Biodemography of Longevity) (1997) 17-37
6. Witten T.M., and Eakin T. Multiphasic models of survival: Background and early developments. Exper. Gerontol. 32 2 (1997) 259-285
7. Finch C.E., Pike M.C., and Witten M. Slow mortality rate accelerations during aging in some animals approximate that of humans. Science 249 (1990) 902-905
8. Witten T.M. Quantifying the concepts of rate and acceleration/deceleration of aging. Growth Dev. Ageing 53 (1989) 7-16
9. Eakin T., and Witten T.M. A gerontological distance metric for analysis of survival dynamics. Mech. Ageing Dev. 78 (1995) 85-101
10. Lakshminarayanan E.S., and Pitchaimani M. Unique estimation of mortality rates in Gompertz survival model parameters. Appl. Math. Lett. 16 2 (2003) 211-219
11. Witten T.M., and Satzer W. Gompertz survival model parameters: Estimation and sensitivity. Appl. Math. Lett. 5#1 (1992) 7-12
12. Shouman R., and Witten M. Survival estimates and sample size: What can we conclude?. J. Gerontol. 50A (1995) B177-B185
13. Comfort A. The Biology of Senescence. 3rd ed. (1979), Elsevier, New York
14. Curtsinger J.W., Fukui H.H., Townsend D.R., and Vaupel J.W. Demography of genototypes: Failure of the limited life-span paradigm in Drosophila melanogaster. Science 258 (1992) 461-463
15. Fukui H.H., Xiu L., and Curtsinger J.W. Slowing of age-specific mortality rates in Drosophila melanogaster. Exp. Gerontol. 28 (1993) 585-599
16. Tatar M., Carey J.R., and Vaupel J.W. Long term cost of reproduction without accelerated senescence in Callosobruchus maculatus: Analysis of age-specific mortality. Evolution 47 (1993) 1302-1312
17. Brooks A., Lithgow G.J., and Johnson T.E. Mortality rates in a genetically heterogeneous population of Caenorhabditis elagans. Science 263 (1994) 668-671
18. Barret J.C. The Mortality of centenarians in England and Wales. Arch. Gerontol. Geriatrics 4 (1985) 211-218
19. Riggs J.E., and Millecchia R.J. Mortality among the elderly in the U.S., 1956-1987: Demonstration of the upper boundary to Gompertzian mortality. Mech. Ageing Dev. 62 (1992) 191-199
20. Hirsch H.R., Liu X., and Witten T.M. Mortality-rate crossovers and maximum lifespan in advantaged and disadvantaged populations: Accelerated mortality and sudden death models. J. Theoret. Biol. 205 (2000) 171-180
21. Wang S., Matsushita T., Kogishi H., Xia C., Chiba T., Hosokawa M., and Higuchi K. Type B apoA - II and SAM. Biomed. Gerontol. 22 (1998) 26
22. Suematsu K., and Kohno M. Age invariant of Gompertz function and exponential decay of populations commensuration with CLOV experiments. J. Theoret. Biol. 201 (1999) 231-238
23. Lakshminarayanan E.S., and Pitchaimani M. Existence of Gompertz parameters and its asymptotic formulae for a large population. Appl. Math. Lett. 17 (2004) 173-180
24. E.S. Lakshminarayanan, M. Pitchaimani, Existence of critical Gompertz parameter and its asymptotic expression, Comput. Math. Appl., in press (doi:10.1016/j.camwa.2007.06.008)
25. Gradshteyn I.S., and Ryzhik I.M. Table of Integrals, Series and Products (1980), Academic Press