Abstract
This paper considers the problem of parameter estimation when data of a random sample are given in the form of a frequency table. We give special consideration to a method that linearizes the cumulative distribution function (CDF). In that case parameters can be derived from the weighted estimation of a linear regression equation. The favourable properties of this estimation technique are demonstrated in a simulation experiment, where the parameters of a two-parameter-Weibull distribution are estimated.
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Carmody, T.J., Eubank, R.L., LaRiccia, V.N. (1984) A family of minimum quantile distance estimators for the three-parameter Weibull distribution. Statistische Hefte, Vol. 25, 69–82.
Cheng, K.F., Chen, C.H. (1988) Estimation of the Weibull parameters with grouped data. Commun. Statist. — Theory Meth., Vol. 17(2), 325–341.
Cox, D.R. and Hinkley, D.V. (1974) Theoretical Statistics. Chapmann and Hall, London.
Gehan, E.A., Siddiqui, M.M. (1973) Simple regression methods for survival time studies. Journal of the American Statistical Association, Vol. 68(344), 848–856.
Johnson, N.L. (1949) Systems of frequency curves generated by methods of translation. Biometrika, Vol. 36, 149–176.
Johnson, N.L, Kotz, S., Balakrishnan N. (1994) Continuous univariate distributions. Vol. 1, 2nd Edition, Wiley, New York.
Lawless, J.F. (1982) Statistical models and methods for lifetime data. Wiley, New York.
McDonald, J.B., Ransom, M.R. (1979) Alternative parameter estimates based upon grouped data. Commun. Statist. — Theory Meth., Vol. A8(9), 899–917.
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Jöhnk, M.D., Niermann, S. Parameter estimation with grouped data according to the linearization method — a comparison with alternative approaches. Statistical Papers 43, 237–255 (2002). https://doi.org/10.1007/s00362-002-0098-7
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DOI: https://doi.org/10.1007/s00362-002-0098-7