A joint confidence region for an overall ranking of populations

The effect of tool-life scatter on the uncertainty of parameters of a typical tool-life model is analyzed using the joint confidence region approach. Some apparent contradictions concerning tool-life test data are explained in terms of their information content in the light of personal probability concepts.

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On Double Value at Risk

Risks ◽

10.3390/risks7010031 ◽

2019 ◽

Vol 7 (1) ◽

pp. 31 ◽

Cited By ~ 1

Author(s):

Wanbing Zhang ◽

Sisi Zhang ◽

Peibiao Zhao

Keyword(s):

At Risk ◽

Value At Risk ◽

Confidence Region ◽

Ratio Method ◽

Two Dimensional ◽

Income Risk ◽

One Dimensional ◽

Joint Confidence Region ◽

The Empirical Analysis ◽

Likelihood Ratio Method

Value at Risk (VaR) is used to illustrate the maximum potential loss under a given confidence level, and is just a single indicator to evaluate risk ignoring any information about income. The present paper will generalize one-dimensional VaR to two-dimensional VaR with income-risk double indicators. We first construct a double-VaR with ( μ , σ 2 ) (or ( μ , V a R 2 ) ) indicators, and deduce the joint confidence region of ( μ , σ 2 ) (or ( μ , V a R 2 ) ) by virtue of the two-dimensional likelihood ratio method. Finally, an example to cover the empirical analysis of two double-VaR models is stated.

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Determination of the joint confidence region of the optimal operating conditions in robust design by the bootstrap technique

International Journal of Production Research ◽

10.1080/00207543.2013.792963 ◽

2013 ◽

Vol 51 (15) ◽

pp. 4695-4703 ◽

Cited By ~ 16

Author(s):

Chanseok Park

Keyword(s):

Robust Design ◽

Confidence Region ◽

Operating Conditions ◽

Optimal Operating ◽

Bootstrap Technique ◽

Joint Confidence Region

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Estimation of the Parameters of the Reversed Generalized Logistic Distribution with Progressive Censoring Data

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2010/539860 ◽

2010 ◽

Vol 2010 ◽

pp. 1-21

Author(s):

Z. A. Abo-Eleneen ◽

E. M. Nigm

Keyword(s):

Shape Parameter ◽

Maximum Likelihood Method ◽

Confidence Region ◽

Likelihood Method ◽

Logistic Distribution ◽

Complete Sample ◽

Generalized Logistic Distribution ◽

Progressive Type ◽

Wide Range ◽

Joint Confidence Region

The reversed generalized logistic (RGL) distributions are very useful classes of densities as they posses a wide range of indices of skewness and kurtosis. This paper considers the estimation problem for the parameters of the RGL distribution based on progressive Type II censoring. The maximum likelihood method for RGL distribution yields equations that have to be solved numerically, even when the complete sample is available. By approximating the likelihood equations, we obtain explicit estimators which are in approximation to the MLEs. Using these approximate estimators as starting values, we obtain the MLEs using iterative method. We examine numerically MLEs estimators and the approximate estimators and show that the approximation provides estimators that are almost as efficient as MLEs. Also we show that the value of the MLEs decreases as the value of the shape parameter increases. An exact confidence interval and an exact joint confidence region for the parameters are constructed. Numerical example is presented in the methods proposed in this paper.

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