Properties of the generalized nonlinear least squares method applied for fitting distribution to data

Mirta Benšić

Discussiones Mathematicae Probability and Statistics (2015)

  • Volume: 35, Issue: 1-2, page 75-94
  • ISSN: 1509-9423

Abstract

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We introduce and analyze a class of estimators for distribution parameters based on the relationship between the distribution function and the empirical distribution function. This class includes the nonlinear least squares estimator and the weighted nonlinear least squares estimator which has been used in parameter estimation for lifetime data (see e.g. [6, 8]) as well as the generalized nonlinear least squares estimator proposed in [3]. Sufficient conditions for consistency and asymptotic normality are given. Capability and limitations are illustrated by simulations.

How to cite

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Mirta Benšić. "Properties of the generalized nonlinear least squares method applied for fitting distribution to data." Discussiones Mathematicae Probability and Statistics 35.1-2 (2015): 75-94. <http://eudml.org/doc/276549>.

@article{MirtaBenšić2015,
abstract = {We introduce and analyze a class of estimators for distribution parameters based on the relationship between the distribution function and the empirical distribution function. This class includes the nonlinear least squares estimator and the weighted nonlinear least squares estimator which has been used in parameter estimation for lifetime data (see e.g. [6, 8]) as well as the generalized nonlinear least squares estimator proposed in [3]. Sufficient conditions for consistency and asymptotic normality are given. Capability and limitations are illustrated by simulations.},
author = {Mirta Benšić},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {generalized least squares; distribution fitting; generalized method of moments; Anderson-Darling statistic; Cramer-von Mises statistic; nonlinear regression; Weibull distribution},
language = {eng},
number = {1-2},
pages = {75-94},
title = {Properties of the generalized nonlinear least squares method applied for fitting distribution to data},
url = {http://eudml.org/doc/276549},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Mirta Benšić
TI - Properties of the generalized nonlinear least squares method applied for fitting distribution to data
JO - Discussiones Mathematicae Probability and Statistics
PY - 2015
VL - 35
IS - 1-2
SP - 75
EP - 94
AB - We introduce and analyze a class of estimators for distribution parameters based on the relationship between the distribution function and the empirical distribution function. This class includes the nonlinear least squares estimator and the weighted nonlinear least squares estimator which has been used in parameter estimation for lifetime data (see e.g. [6, 8]) as well as the generalized nonlinear least squares estimator proposed in [3]. Sufficient conditions for consistency and asymptotic normality are given. Capability and limitations are illustrated by simulations.
LA - eng
KW - generalized least squares; distribution fitting; generalized method of moments; Anderson-Darling statistic; Cramer-von Mises statistic; nonlinear regression; Weibull distribution
UR - http://eudml.org/doc/276549
ER -

References

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