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

Nonlinear least squares procedures for estimating the parameters of the shifted Gompertz distribution are proposed. Simulation studies are carried out to compare weighted and unweighted least squares methods, the maximum likelihood method and method of moments. This work concludes that least squares methods via weighting factors to estimate the parameters of this probability distribution give a better performance than unweighted least squares methods, showing the importance of weighting factors. Besides, results of this simulation study show that a good performance is obtained using the maximum likelihood method and the estimators obtained with more bias are those of the method of moments.

[1]  Jong-Wuu Wu,et al.  A Note on Weighted Least‐squares Estimation of the Shape Parameter of the Weibull Distribution , 2004 .

[2]  Bill Bergman.  Estimation of Weibull parameters using a weight function , 1986 .

[3]  Liang Peng,et al.  REGRESSION MODELING FOR NONPARAMETRIC ESTIMATION OF DISTRIBUTION AND QUANTILE FUNCTIONS , 2002 .

[4]  G. Lilien,et al.  Bias and Systematic Change in the Parameter Estimates of Macro-Level Diffusion Models , 1997 .

[5]  The Estimation of Pareto Distribution by a Weighted Least Square Method , 2007 .

[6]  A. Öztürk,et al.  Least Squares Estimation of the Parameters of the Generalized Lambda Distribution , 1985 .

[7]  V. Barnett.  Probability Plotting Methods and Order Statistics , 1975 .

[8]  Yoshihiro Tohma,et al.  The Estimation of Parameters of the Hypergeometric Distribution and Its Application to the Software Reliability Growth Model , 1991, IEEE Trans. Software Eng..

[9]  Jr William P. Putsis.  Parameter variation and new product diffusion , 1998 .

[10]  Yuan-Chen Liu,et al.  Estimation Of Weibull Parameters Using A Fuzzy Least-Squares Method , 2005, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[11]  Peter Teunissen,et al.  Nonlinear least squares , 1990 .

[12]  G. Lilien,et al.  Erratum to Bias and Sysematic Change in the Parameter Estimates of Macro-Level Diffusion Models , 1998 .

[13]  R. L. Eubank,et al.  A Density-Quantile Function Approach to Optimal Spacing Selection , 1981 .

[14]  Charlotte H. Mason,et al.  Technical Note---Nonlinear Least Squares Estimation of New Product Diffusion Models , 1986 .

[15]  Frank M. Bass,et al.  A New Product Growth for Model Consumer Durables , 2004, Manag. Sci..

[16]  P. Jodrá,et al.  A Note on the Moments and Computer Generation of the Shifted Gompertz Distribution , 2008 .

[17]  Rudolf Scitovski,et al.  Solving parameter estimation problem in new product diffusion models , 2002, Appl. Math. Comput..

[18]  Ronald L. Wasserstein,et al.  Monte Carlo: Concepts, Algorithms, and Applications , 1997 .

[19]  D. A. Barry,et al.  Analytical approximations for real values of the Lambert W -function , 2000 .

[20]  Gaston H. Gonnet,et al.  On the LambertW function , 1996, Adv. Comput. Math..

[21]  P. Bickel,et al.  Mathematical Statistics: Basic Ideas and Selected Topics , 1977 .

[22]  Pandu R. Tadikamalla,et al.  A Probability Distribution and its Uses in Fitting Data , 1979 .

[23]  Albert C. Bemmaor.  Modeling the Diffusion of New Durable Goods: Word-of-Mouth Effect Versus Consumer Heterogeneity , 1992 .

[24]  Dragan Jukić,et al.  Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start , 2009 .

[25]  Xinlong Feng,et al.  Estimation of parameters of the Makeham distribution using the least squares method , 2008, Math. Comput. Simul..

[26]  Vijay Mahajan,et al.  Maximum Likelihood Estimation for an Innovation Diffusion Model of New Product Acceptance , 1982 .

[27]  Ralph B. D'Agostino,et al.  Goodness-of-Fit-Techniques , 2020 .

[28]  F. Bass.  A new product growth model for consumer durables , 1976 .

[29]  William P. Putsis.  Temporal aggregation in diffusion models of first-time purchase: Does choice of frequency matter? , 1996 .

[30]  Jong-Wuu Wu,et al.  Estimation of parameters of the Gompertz distribution using the least squares method , 2004, Appl. Math. Comput..

[31]  Tekin Öztekin,et al.  Estimation of the Parameters of Wakeby Distribution by a Numerical Least Squares Method and Applying it to the Annual Peak Flows of Turkish Rivers , 2011 .