Estimation of parameters of the shifted Gompertz distribution using least squares, maximum likelihood and moments methods

Journal of Computational and Applied Mathematics

Volumn 255, Issue , 2014, Pages 867-877

  Jiménez Torres, Fernando ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

Gompertz distribution; Least squares estimation; Maximum likelihood estimation; Moment estimation; Quantile function; Shifted; Simulation

Indexed keywords

GOMPERTZ DISTRIBUTIONS; LEAST SQUARES ESTIMATION; MOMENT ESTIMATION; QUANTILE FUNCTIONS; SHIFTED; SIMULATION;

LEAST SQUARES APPROXIMATIONS; MAXIMUM LIKELIHOOD ESTIMATION; METHOD OF MOMENTS; PROBABILITY DISTRIBUTIONS;

PARAMETER ESTIMATION;

EID: 84881273866     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2013.07.004     Document Type: Article

References (30)

1. F.M. Bass A new product growth model for consumer durables Manage. Sci. 15 1969 215 227
2. A.C. Bemmaor Modeling the diffusion of new durable goods: word-of-mouth effect versus consumer heterogeneity G. Laurent, G.L. Lilien, B. Pras, Research Traditions in Marketing 1994 Kluwer MA, Boston 201 223
3. F. Jiménez, and P. Jodrá A note on the moments and computer generation of the shifted Gompertz distribution Comm. Statist. Theory Methods 38 2009 75 89
4. W.P. Putsis Jr. Temporal aggregation in diffusion models of first-time purchase: does choice of frequency matter? Technol. Forecast. Soc. Change 51 1996 265 279
5. V. Srinivasan, and C.H. Mason Nonlinear least squares estimation of new product diffusion models Mark. Sci. 5 2 1986 169 178
6. V. Mahajan, C.H. Mason, and V. Srinivasan An evaluation of estimation procedures for new product diffusion models V. Mahajan, Y. Wind, Innovation Diffusion Models of New Product Acceptance 1986 Ballinger Cambridge 203 232
7. D.C. Schmittlein, and V. Mahajan Maximum likelihood estimation for an innovation diffusion model of new product acceptance Mark. Sci. 1 1 1982 57 78
8. R. Scitovski, and M. Meler Solving parameter estimation problem in new product diffusion models Appl. Math. Comput. 127 1 2002 45 63 (Pubitemid 34116069)
9. W.P. Putsis Jr. Parameter variation and new product diffusion J. Forecast. 17 1998 231 257 (Pubitemid 128688258)
10. C. Van den Bulte, and G.L. Lilien Bias and systematic change in the parameter estimates of macro-level diffusion models Mark. Sci. 16 4 1997 338 353
11. J.S. Ramberg, P.R. Tadikamalla, E.J. Dudewicz, and E.F. Mykytka A probability distribution and its uses in fitting data Technometrics 21 2 1979 201 214
12. A. Öztürk, and R.F. Dale Least squares estimation of the parameters of the generalized lambda distribution Technometrics 27 1 1985 81 84 (Pubitemid 15454292)
13. Y. Tohma, H. Yamano, M. Ohba, and R. Jacoby The estimation of parameters of the hypergeometric distribution and its application to the software reliability growth model IEEE Trans. Softw. Eng. 17 5 1991 483 489 (Pubitemid 21676227)
14. H. Lu, C. Chen, and J. Wu A note on weighted least-squares estimation of the shape parameter of the Weibull distribution Qual. Reliab. Eng. Int. 20 2004 579 586
15. W.-L. Hung, and Y.-C. Liu Estimation of Weibull parameters using a fuzzy least-squares method Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 12 5 2004 701 711
16. D. Markovic, D. Jukic, and M. Bensic Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start J. Comput. Appl. Math. 228 2009 304 312
17. J. Wu, W. Hung, and C. Tsai Estimation of parameters of the Gompertz distribution using the least squares method Appl. Math. Comput. 158 2004 133 147
18. H. Lu, and S. Tao The estimation of Pareto distribution by a weighted least square method Qual. Quant. 41 2007 913 926
19. X. Feng, G. He, and Abdurishit Estimation of parameters of the Makeham distribution using the least squares method Math. Comput. Simul. 77 2008 34 44 (Pubitemid 351173526)
20. T. Öztekin Estimation of the parameters of Wakeby distribution by a numerical least squares method and applying it to the annual peak flows of Turkish rivers Water Resour. Res. 25 5 2011 1299 1313
21. R.B. D'Agostino, and M.A. Stephens Goodness-of-Fit Techniques 1986 Marcel Dekker New York 25
22. V. Barnett Probability plotting methods and order statistics Appl. Stat. 24 1 1975 95 108
23. B. Bergman Estimation of Weibull parameters using a weight function J. Mater. Sci. Lett. 5 1986 611 614 (Pubitemid 16586922)
24. P.J. Bickel, and K.A. Doksum Mathematical Statistics-Basic Ideas and Selected Topics. Vol. I 2001 Prentice-Hall Englewood Cliffs, NJ 316 317
25. R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey, and D.E. Knuth On the Lambert W function Adv. Comput. Math. 5 1996 329 359 (Pubitemid 126729167)
26. D.A. Barry, J.-Y. Parlange, L. Li, H. Prommer, C.J. Cunningham, and F. Stagnitti Analytical approximations for real values of the Lambert W-function Math. Comput. Simul. 15 2000 95 103
27. R.L. Eubank A density-quantile function approach to optimal spacing selection Ann. Statist. 9 3 1981 494 500
28. M. Cheng, and L. Peng Regression modeling for nonparametric estimation of distribution and quantile functions Statist. Sinica 12 2002 1043 1060 (Pubitemid 36116665)
29. G.S. Fishman Monte Carlo: Concepts, Algorithms and Applications 1996 Springer-Verlag New York 149 156
30. J.E. Dennis Jr., and R.B. Schnabel Nonlinear least squares Numerical Methods for Unconstrained Optimization and Nonlinear Equations 1996 SIAM Philadelphia, PA 218 238