engleski

Fitting distribution to data by a generalized nonlinear least squares method

The primary concern is to introduce and illustrate the way of using a generalized nonlinear regression method for the purpose of parameter estimation in the classical parametric independent and identically distributed sample model. It is shown by simulation that the presented estimator has a root mean square error comparable to the maximum likelihood estimator in the model for which it is known that maximum likelihood has excellent properties. As this estimator is based on an empirical distribution function, it is also compared to the maximum goodness-of-fit estimators that minimize Cramer-von Mises and Anderson- Darling empirical distribution statistics and it is shown that it outperforms them in most cases.

Generalized least squares; nonlinear regression; Anderson-Darling statistic; Cramer-von Mises statistic; Weibull distribution

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