ESTIMATION OF PARAMETERS FOR THE LIFETIME DISTRIBUTIONS
DOI:
https://doi.org/10.13052/jrss2229-5666.1227Keywords:
Lifetime Distributions, Methods of Estimation, Goodness of Fit Analysis, SimulationAbstract
This paper deals with various methods of estimation used for estimating the parameters of lifetime distributions. The distributions considered are exponential, Weibull, Rayleigh, lognormal and gamma and the method used are: method of moments, maximum likelihood, probability weighted moments, least squares and relative least squares. To compare the efficiency between the different methods of estimation, we used the total deviation, mean squared error and probability plot correlation coefficients. In order to study numerically, the execution of the different methods of estimation and goodness of fit analysis, their statistical properties have been simulated for different sample sizes. The graphs of bias designed for different methods of estimation have also been plotted against various sample sizes.
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References
Afify, E.E. (2003).Comparison of estimators of parameters for the rayleigh distribution, Faculty of Eng. Shibeen El Kom Menoufia Univ.
Castillo, E. and Hadi, A.S. (1997). Fitting the generalized Pareto distribution to data, J. Amer. Stat. Assoc., 9, p. 1609-1620.
Deshpande, J.V. and Purohit, S.G. (2001). Survival, hazard and competing risks. Current. Sci., 80(9), p. 1190-1202.
DeZea Bermudez, P. and Amaral Turkman, M. A. (2003). bayesian approach to parameter estimation of the generalized pareto distribution, Sociedad Espemolade Estadisticae Investigacion Operativa Test, 12(1), p. 259-277.
Epstein, B., and Sobel, M. (1953). Life testing, Journal of the American Statistical Association, 48, p.486:502.
Grimshaw, S.D. (1993). Computing maximum likelihood estimates for the generalized Pareto distribution, Technometrics, 35, p. 185-191.
Hirai, A.S., (1998). A Course in Mathematical Statistics, Illami Kitab Khana, Lahore, Pakistan, p. 663-665.
Hosking, J.R.M. and Wallis, J.R. (1987). Parameter and quantile estimation for the generalized Pareto distribution, Technometrics, 29(3), p. 339-349.
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, Vol. I, II Ed. John Wiley and Sons Inc., p.628-636.
Klein,J.P. and Moeshberger,M.L.(1997). Survival Analysis: Techniques for Censored and Truncated Data, New York: Springer.
Lee,L. and Thompson, W.A. (1956). Results on a failure time and pattern for the series system. In Reliability and Biometry. Statistical Analysis of Life Length: SIAM, p. 292-302.
Linhart,H. and Zucchini,W. (1986). Model Selection. Wiley, NewYork.
Mahdi, S. and Cenac, M. (2006). Estimating and assessing the parameters of Rayleigh distributions from three methods of estimation, Caribb. J. Math. Comput. Sci, 13, p. 25-34.
Weibull, W. (1939a). A statistical theory of the strength of material. report No.151, Ingeniorsvetenskaps, AkademiensHandligar, Stockholm.
Weibull, W. (1939b). The phenomena of rapture in solids. Report No.153, Ingeniorsvetenskaps, AkademiensHandligar, Stockholm.
Weibull, W. (1951). A statistical distribution of wide applicability, Journal of Applied Mechanics, 18, p. 293-297.
