Estimation of parameters of the Makeham distribution using the least squares method

Mathematics and Computers in Simulation

Volumn 77, Issue 1, 2008, Pages 34-44

  Feng, Xinlong ^a,b   He, Guoliang ^b   Abdurishit, ^a  

^a XINJIANG UNIVERSITY   (China)

^b XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Least squares estimation; Makeham distribution; Parameter; Reliability

Indexed keywords

FUNCTIONS; HAZARDS; LEAST SQUARES APPROXIMATIONS; MEAN SQUARE ERROR;

ESTIMATORS; HUMAN MORTALITY; LEAST SQUARES ESTIMATION; MAKEHAM DISTRIBUTION;

PARAMETER ESTIMATION;

EID: 38649131268     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2007.01.009     Document Type: Article

References (23)

1. Asmussena S., and Moller J.R. Risk comparisons of premium rules: optimality and a life insurance study. Insur. Math. Econ. 32 3 (2003) 331-344
2. Bain L. Analysis for the linear failure-rate life testing distribution. Technometrics 15 4 (1974) 551-559
3. Balakrishnan N., and Malik H. Order statistics from the linear exponential distribution. I. Increasing hazard rate case. Commun. Stat.-Theory Methods 15 11 (1986) 179-203
4. Balasooriya U. Failure-censored reliability sampling plans for the exponential distribution. J. Stat. Comput. Simul. 52 (1995) 337-349
5. Bernhard K. A class of tests for exponentiality against HNBUE alternatives. Stat. Probab. Lett. 47 (2000) 199-207
6. Debon A., Montes F., and Sala R. A comparison of models for dynamic life tables. Application to mortality data from the Valencia Region (Spain). Lifetime Data Anal. 12 2 (2006) 223-244
7. Drapella A. An improved failure-free time estimation method. Qual. Reliab. Eng. Int. 15 3 (1999) 235-238
8. Gavrilov L.A., and Gavrilova N.S. The reliability theory of aging and longevity. J. Theor. Biol. 213 (2001) 527-545
9. Golubev A. Does Makeham make sense?. Biogerontology 5 (2004) 159-167
10. Lakshminarayanan E.S., and Pitchaimani M. Unique estimation of mortality rates in Gompertz survival model parameters. Appl. Math. Lett. 16 (2003) 211-219
11. Lin C., Wu S., and Balakrishnan N. Parameter estimation for the linear hazard rate distribution based on records and inter-record times. Commun. Stat.-Theory Methods 32 4 (2003) 729-748
12. Makeham W.M. On the law of mortality and the construction of annuity tables. J. Inst. Actuaries 13 (2000) 325-358
13. Miklavcic D., Jarm T., Karba R., and Sersa G. Mathematical modelling of tumor growth in mice following electrotherapy and bleomycin treatment. Math. Comput. Simulat. 39 (1995) 597-602
14. Moustafa H.M., and Ramadan S.G. Errors of misclassication and their probability distributions when the parent populations are Gompertz. Appl. Math. Comput. 163 (2005) 423-442
15. Mugdadi A.R. The least squares type estimation of the parameters in the power hazard function. Appl. Math. Comput. 169 (2005) 737-748
16. Norberg R. Differential equations for moments of present values in life insurance. Insur. Math. Econ. 17 (1995) 171-180
17. Poschet F., Bernaerts K., et al. Sensitivity analysis of microbial growth parameter distributions with respect to data quality and quantity by using Monte Carlo analysis. Math. Comput. Simulat. 65 (2004) 231-243
18. Scollnik D.P.M. Simulating random variates from Makeham's distribution and from others with exact or nearly Log-Concave densities. Trans. Soc. Actuaries 47 (1995) 409-437
19. Sen A., and Bhattacharyya G. Inference procedures for the linear failure rate model. J. Stat. Plan. Inference 46 (1995) 59-76
20. Sithole T.Z., Haberman S., and Verrall R.J. An investigation into parametric models for mortality projections, with applications to immediate annuitants' and life office pensioners' data. Insur. Math. Econ. 27 (2000) 285-312
21. Wu J.W., Hung W.L., and Tsai C.H. Estimation of parameters of the Gompertz distribution using the least squares method. Appl. Math. Comput. 158 (2004) 133-147
22. Wu J.W., and Li P.L. Optimal estimation of the parameters of the Gompertz distribution based on the doubly type II censored sample. Qual. Quant. 38 (2004) 753-769
23. Wu C.C., Wu S.F., and Chan H.Y. MLE and the estimated expected test time for the two-parameter Gompertz distribution under progressive censoring with binomial removals. Appl. Math. Comput. 181 (2006) 1657-1670