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Title: The application of a new method of parameter estimation to the three-parameter lognormal and the three-parameter weibull distributions
Author: Amin, N. A. K.
Awarding Body: University of Wales Institute of Science and Technology
Current Institution: Cardiff University
Date of Award: 1981
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A new method of parameter estimation similar to maximum likelihood(ML) estimation is proposed to overcome the problem associated with the unbounded likelihood in ML estimation when applied to distributions such as the 3-parameter lognormal and the 3-parameter Weibull models. Tn-. these distributions, ML estimation often breaks down with unresolved theoretical and practical difficulties, but the new method yields efficient estimators for all values in the parameter space. Unlike the ad hoe modifications sometimes applied to obtain usable estimators in ML method, this method is based on a general principle applicable to any continuous univariate distribution. It gives consistent estimators under more general conditions'than ML. In regular situation, the new estimators are asymptotically normal and efficient. Moreover, in non-standard situation, tfle new estimation yields efficient estimators even when ML estimation fails. An extensive Monte Carlo study is carried out to compare the performance of the new method and NIT; method in the above 3-parameter distributions for a series o-'-* sample sizes e-nd parameter values. Iterative procedures are suSgested for computing the estimates which include a 1goodness of fit test of the model before estimation. The Mon-1-e1 Carlo results indicate -that variances of the new estimators are similar to those of the ML estimators. An exception is in very skewe. d samples where, while the ML estimatior is bound to fail, this method gives more efficient estimators.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Applied statistics Mathematical statistics Operations research