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Articles

The moments of the Gompertz distribution and maximum likelihood estimation of its parameters

Pages 255-277 | Received 20 Jan 2012, Accepted 18 Apr 2012, Published online: 21 May 2012

References

  • Abramowitz , M. and Stegun , I. 1965 . Handbook of mathematical functions , Washington , DC : US Government Printing Office .
  • Apéry , R. 1979 . Irrationalité de ζ (2) et ζ (3) . Astérisque , 61 : 11 – 13 .
  • Askey , R. A. and Daalhuis , A. B. O. 2010 . “ Generalized hypergeometric functions and Meijer G-Function ” . In NIST handbook of mathematical functions , Edited by: Olver , F. , Lozier , D. , Boisvert , R. and Clark , C. 403 – 418 . Cambridge : Cambridge University Press .
  • Erdélyi , A. 1953 . Higher transcendental functions, vol. 1 , New York–Toronto–London : McGraw-Hill .
  • Fisher , R. and Tippett , L. 1928 . Limiting forms of the frequency distribution of the largest or smallest member of a sample . Mathematical Proceedings of the Cambridge Philosophical Society , 24 ( 2 ) : 180 – 190 .
  • Garg , M. , Rao , B. and Redmond , C. 1970 . Maximum-likelihood estimation of the parameters of the Gompertz survival function . Journal of the Royal Statistical Society. Series C (Applied Statistics) , 19 ( 2 ) : 152 – 159 .
  • Gompertz , B. 1825 . 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 . Philosophical Transactions of the Royal Society of London , 115 : 513 – 583 .
  • Greene , W. 2003 . Econometric analysis , 5th edn , New Jersey : Prentice-Hall .
  • Gussmann , E. 1967 . Modifizierung der Gewichtsfunktionenmethode zur Berechnung der Fraunhoferlinien in Sonnen-und Sternspektren . Zeitschrift für Astrophysik , 65 : 456 – 497 .
  • Hansen , L. 1982 . Large sample properties of generalized method of moments estimators . Econometrica , 50 ( 4 ) : 1029 – 1054 .
  • Kunimura , D. 1998 . The Gompertz distribution-estimation of parameters . Actuarial Research Clearing House , 2 : 65 – 76 .
  • Marshall , A. and Olkin , I. 2007 . Life distributions , New York : Springer .
  • Milgram , M. 1985 . The generalized integro-exponential function . Mathematics of Computation , 44 ( 170 ) : 443 – 458 .
  • Missov , T. and Lenart , A. 2011 . Linking period and cohort life-expectancy linear increases in Gompertz proportional hazards models . Demographic Research , 24 ( 19 ) : 455 – 468 .
  • Pollard , J. and Valkovics , E. 1992 . The Gompertz distribution and its applications . Genus , 48 ( 3–4 ) : 15 – 29 .
  • Pollard , J. and Valkovics , E. 1997 . On the use of the truncated Gompertz distribution and other models to represent the parity progression functions of high fertility populations . Mathematical Population Studies , 6 ( 4 ) : 291 – 305 .
  • Preston , S. , Heuveline , P. and Guillot , M. 2001 . Demography: measuring and modeling population processes , Oxford and Malden , MA : Wiley-Blackwell .
  • Tan , W. and Chang , W. 1972 . Some comparisons of the method of moments and the method of maximum likelihood in estimating parameters of a mixture of two normal densities . Journal of the American Statistical Association , 67 ( 339 ) : 702 – 708 .
  • Tawn , J. 1990 . Modelling multivariate extreme value distributions . Biometrika , 77 ( 2 ) : 245 – 253 .
  • Vaupel , J. 1986 . How change in age-specific mortality affects life expectancy . Population Studies , 40 ( 1 ) : 147 – 157 .
  • Vaupel , J. 2010 . Biodemography of human ageing . Nature , 464 ( 7288 ) : 536 – 542 .
  • Wetterstrand , W. 1981 . Parametric models for life insurance mortality data: Gompertz's law over time . Transactions of the Society of Actuaries , 33 : 159 – 175 .
  • Wilks , S. 1962 . Mathematical statistics , New York : John Wiles & Sons .
  • Willekens , F. 2002 . “ Gompertz in context: the Gompertz and related distributions ” . In Forecasting mortality in developed countries – insights from a statistical, demographic and epidemiological perspective, European studies of population , Edited by: Tabeau , E. , van den Berg Jeths , A. and Heathcote , C. Vol. 9 , 105 – 126 . Dordrecht : Kluwer Academic Publishers .
  • Willemse , W. and Koppelaar , H. 2000 . Knowledge elicitation of Gompertz’ law of morality . Scandinavian Actuarial Journal , 2000 ( 2 ) : 168 – 180 .
  • Wilmoth , J. , Andreev , K. , Jdanov , D. & Glei , D. 2007 . Methods protocol for the Human Mortality Database . University of California, Berkeley, and Max Planck Institute for Demographic Research, Rostock. http://www.mortality.org/Public/Docs/MethodsProtocol.pdf .

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