References
- Abramowitz M. and Stegun I.A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables . Dover , New York , 1972 .
- Arnold B.C. , Balakrishnan N. and Nagaraja H.N. A First Course in Order Statistics . Wiley Ser. Probab. Math. Stat . John Wiley & Sons Inc. , New York , 1992 .
- Balakrishnan N. and Rao C.R. (Eds.). Handbook of Statistics, vol. 16, Order Statistics: Theory and Methods . Elsevier , Amsterdam , 1998 .
- Castillo , E. , Hadi , A.S. , Balakrishnan , N. and Sarabia , J.M. 2005 . Extreme Value and Related Models with Applications in Engineering and Science , Hoboken , NJ : Wiley .
- Chan , L.K. 1967 . On a characterization of distributions by expected values of extreme order statistics . Amer. Math. Monthly , 74 ( 8 ) : 950 – 951 . http://dx.doi.org/10.2307/2315271
- Corless , R.M. , Gonnet , G.H. , Hare , D.E.G. , Jeffrey , D.J. and Knuth , D.E. 1996 . On the Lambert W function . Adv. Comput. Math. , 5 ( 4 ) : 329 – 359 . http://dx.doi.org/10.1007/BF02124750
- Feng , X. , He , G. and Abdurishit . 2008 . Estimation of parameters of the Makeham distribution using the least squares method . Math. Comput. Simulation , 77 ( 1 ) : 34 – 44 .
- Galambos , J. 1987 . The Asymptotic Theory of Extreme Order Statistics , 2nd edition , Melbourne : Krieger Publishing Co .
- Golubev , A. 2004 . Does Makeham make sense? . Math. Comput. Simulation , 5 ( 3 ) : 159 – 167 .
- Hoorfar A. and Hassani M. Inequalities on the Lambert W function and hyperpower function , J. Inequal. Pure Appl. Math. , 9 , 2008 . Art. 51
- Huang , J.S. 1989 . Moment problem of order-statistics: A review . Int. Stat. Rev. , 57 ( 1 ) : 59 – 66 . http://dx.doi.org/10.2307/1403584
- Jodrá , P. 2009 . A closed-form expression for the quantile function of the Gompertz- Makeham distribution . Math. Comput. Simulation , 79 ( 10 ) : 3069 – 3075 . http://dx.doi.org/10.1016/j.matcom.2009.02.002
- Kotz , S. and Nadarajah , S. 2000 . Extreme Value Distributions. Theory and Applications , London : Imperial College Press .
- Lagerås , A.N. 2010 . Commutations functions under Gompertz-Makeham mortality . Scand. Actuar. J. , 2 : 161 – 164 . http://dx.doi.org/10.1080/03461230903344181
- Lenart A. The moments of the Gompertz distribution and maximum likelihood estimation of its parameters . Scand. Actuar. J., 2013 . http://dx.doi.org/10.1080/00949655.2012.744406 To appear .
- Makeham , W.M. 1860 . On the law of mortality and the construction of annuity tables . J. Inst. Actuaries , 8 ( 6 ) : 301 – 310 .
- Marshall , A.W. and Olkin , I. 2007 . Life Distributions. Structure of Nonparametric, Semiparametric, and Parametric Families , New York : Springer .
- Milgram , M.S. 1985 . The generalized integro-exponential function . Math. Comp. , 44 ( 170 ) : 443 – 458 . http://dx.doi.org/10.1090/S0025-5718-1985-0777276-4
- Promislow , D.E.L. and Haselkorn , T.S. 2002 . Age-specific metabolic rates and mortality rates in the genus Drosophila . Aging Cell , 1 ( 1 ) : 66 – 74 . http://dx.doi.org/10.1046/j.1474-9728.2002.00009.x
- Teimouri , M. and Gupta , A.K. 2012 . Estimation methods for the Gompertz-Makeham distribution under progressively type-I interval censoring scheme . Natl. Acad. Sci. Lett. , 35 ( 3 ) : 227 – 235 . http://dx.doi.org/10.1007/s40009-012-0048-4