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Conditional Confidence Interval for the Scale Parameter of a Weibull Distribution

Mahdi, Smail (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 62F25, 62F03.A two-sided conditional confidence interval for the scale parameter θ of a Weibull distribution is constructed. The construction follows the rejection of a preliminary test for the null hypothesis: θ = θ0 where θ0 is a given value. The confidence bounds are derived according to the method set forth by Meeks and D’Agostino (1983) and subsequently used by Arabatzis et al. (1989) in Gaussian models and more recently by Chiou and Han (1994, 1995)...

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.

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