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Confidence regions in nonlinear regression models

Rastislav Potocký, Van Ban To (1992)

Applications of Mathematics

New curvature measures for nonlinear regression models are developed and methods of their computing are given. Using these measures, more accurate confidence regions for parameters than those based on linear or quadratic approximations are obtained.

Confidence regions of minimal area for the scale-location parameter and their applications

A. Czarnowska, A. V. Nagaev (2001)

Applicationes Mathematicae

The area of a confidence region is suggested as a quality exponent of parameter estimation. It is shown that under very mild restrictions imposed on the underlying scale-location family there exists an optimal confidence region. Explicit formulae as well as numerical results concerning the normal, exponential and uniform families are presented. The question how to estimate the quantile function is also discussed.

Estimation functions and uniformly most powerful tests for inverse Gaussian distribution

Ion Vladimirescu, Radu Tunaru (2003)

Commentationes Mathematicae Universitatis Carolinae

The aim of this article is to develop estimation functions by confidence regions for the inverse Gaussian distribution with two parameters and to construct tests for hypotheses testing concerning the parameter λ when the mean parameter μ is known. The tests constructed are uniformly most powerful tests and for testing the point null hypothesis it is also unbiased.

Inference on overlap coefficients under the Weibull distribution : equal shape parameter

Obaid Al-Saidy, Hani M. Samawi, Mohammad F. Al-Saleh (2005)

ESAIM: Probability and Statistics

In this paper we consider three measures of overlap, namely Matusia’s measure ρ , Morisita’s measure λ and Weitzman’s measure Δ . These measures are usually used in quantitative ecology and stress-strength models of reliability analysis. Herein we consider two Weibull distributions having the same shape parameter and different scale parameters. This distribution is known to be the most flexible life distribution model with two parameters. Monte Carlo evaluations are used to study the bias and precision...

Inference on overlap coefficients under the Weibull distribution: Equal shape parameter

Obaid Al-Saidy, Hani M. Samawi, Mohammad F. Al-Saleh (2010)

ESAIM: Probability and Statistics

In this paper we consider three measures of overlap, namely Matusia's measure ρ, Morisita's measure λ and Weitzman's measure Δ. These measures are usually used in quantitative ecology and stress-strength models of reliability analysis. Herein we consider two Weibull distributions having the same shape parameter and different scale parameters. This distribution is known to be the most flexible life distribution model with two parameters. Monte Carlo evaluations are used to study the bias and precision...

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