Interval Estimates for Probabilities of Non-Perforation Derived From a Generalized Pivotal Quantity

2005 ◽  
Author(s):  
David W. Webb
Keyword(s):  
Pivotal Quantity ◽  
Interval Estimates ◽  
Generalized Pivotal Quantity

Constructing a confidence interval for the ratio of normal distribution quantiles

2020 ◽  
Vol 26 (4) ◽  
pp. 325-334
Author(s):  
Ahad Malekzadeh ◽  
Seyed Mahdi Mahmoudi
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Intervals ◽  
Pivotal Quantity ◽  
Simple Method ◽  
Normal Populations ◽  
Generalized Pivotal Quantity ◽  
Variance Estimate

AbstractIn this paper, to construct a confidence interval (general and shortest) for quantiles of normal distribution in one population, we present a pivotal quantity that has non-central t distribution. In the case of two independent normal populations, we propose a confidence interval for the ratio of quantiles based on the generalized pivotal quantity, and we introduce a simple method for extracting its percentiles, based on which a shorter confidence interval can be created. Also, we provide general and shorter confidence intervals using the method of variance estimate recovery. The performance of five proposed methods will be examined by using simulation and examples.

scholarly journals Validation and Measurement Uncertainty Assessment of a Microbiological Method Using Generalized Pivotal Quantity Procedure and Monte-Carlo Simulation

2018 ◽  
Vol 101 (4) ◽  
pp. 1205-1211
Author(s):  
Saad Alaoui Sossé ◽  
Taoufiq Saffaj ◽  
Bouchaib Ihssane
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Measurement Uncertainty ◽  
Uncertainty Assessment ◽  
Tolerance Interval ◽  
Alternative Procedure ◽  
Pivotal Quantity ◽  
Statistical Tool ◽  
Generalized Pivotal Quantity ◽  
Escherichia Coli Bacteria

Abstract Recently, a novel and effective statistical tool called the uncertainty profile has been developed with the purpose of graphically assessing the validity and estimating the measurement uncertainty of analytical procedures. One way to construct the uncertainty profile is to compute the β-content, γ-confidence tolerance interval. In this study, we propose a tolerance interval based on the combination of the generalized pivotal quantity procedure and Monte-Carlo simulation. The uncertainty profile has been applied successfully in several fields. However, in order to further confirm its universality, this newer approach has been applied to assess the performance of an alternative procedure versus a reference procedure for counting of Escherichia coli bacteria in drinking water. Hence, the aims of this research were to expose how the uncertainty profile can be powerfully applied pursuant to ISO 16140 standards in the frame of interlaboratory study and how to easily make a decision concerning the validity of the procedure. The analysis of the results shows that after the introduction of a correction factor, the alternative procedure is deemed valid over the studied range because the uncertainty limits lie within the acceptability limits set at ±−0.3 log unit/100 ml for a β = 66.7% and γ = 90%.

A generalized pivotal quantity approach to portfolio selection

2016 ◽  
Vol 44 (8) ◽  
pp. 1402-1420 ◽  
Author(s):  
Philip L.H. Yu ◽  
Thomas Mathew ◽  
Yuanyuan Zhu
Keyword(s):  
Portfolio Selection ◽  
Pivotal Quantity ◽  
Generalized Pivotal Quantity

scholarly journals Equivariance and Generalized Inference in Two-Sample Location-Scale Families

2011 ◽  
Vol 2011 ◽  
pp. 1-16
Author(s):  
Sévérien Nkurunziza ◽  
Fuqi Chen
Keyword(s):  
Monte Carlo Simulation ◽  
Maximum Likelihood Estimators ◽  
Conditional Inference ◽  
Simulation Studies ◽  
Pivotal Quantity ◽  
Minimum Risk ◽  
Generalized Pivotal Quantity ◽  
Location Parameters ◽  
Generalized Inference ◽  
The Difference

We are interested in-typical Behrens-Fisher problem in general location-scale families. We present a method of constructing generalized pivotal quantity (GPQ) and generalizedPvalue (GPV) for the difference between two location parameters. The suggested method is based on the minimum risk equivariant estimators (MREs), and thus, it is an extension of the methods based on maximum likelihood estimators and conditional inference, which have been, so far, applied to some specific distributions. The efficiency of the procedure is illustrated by Monte Carlo simulation studies. Finally, we apply the proposed method to two real datasets.

How to Correct for Chance Agreement in the Estimation of Sensitivity and Specificity of Diagnostic Tests

1994 ◽  
Vol 33 (02) ◽  
pp. 180-186 ◽  
Author(s):  
H. Brenner ◽  
O. Gefeller
Keyword(s):  
Sensitivity And Specificity ◽  
Disease Status ◽  
Disease Prevalence ◽  
Small Sample ◽  
Small Samples ◽  
Interval Estimate ◽  
Traditional Concept ◽  
Interval Estimates ◽  
Major Disadvantage ◽  
Test Result

Abstract:The traditional concept of describing the validity of a diagnostic test neglects the presence of chance agreement between test result and true (disease) status. Sensitivity and specificity, as the fundamental measures of validity, can thus only be considered in conjunction with each other to provide an appropriate basis for the evaluation of the capacity of the test to discriminate truly diseased from truly undiseased subjects. In this paper, chance-corrected analogues of sensitivity and specificity are presented as supplemental measures of validity, which pay attention to the problem of chance agreement and offer the opportunity to be interpreted separately. While recent proposals of chance-correction techniques, suggested by several authors in this context, lead to measures which are dependent on disease prevalence, our method does not share this major disadvantage. We discuss the extension of the conventional ROC-curve approach to chance-corrected measures of sensitivity and specificity. Furthermore, point and asymptotic interval estimates of the parameters of interest are derived under different sampling frameworks for validation studies. The small sample behavior of the estimates is investigated in a simulation study, leading to a logarithmic modification of the interval estimate in order to hold the nominal confidence level for small samples.

Neyman-Pearson and Bayes Interval Estimates for Sampling by Atiributes

1984 ◽  
Vol 31 (6) ◽  
pp. 1576-1579
Author(s):  
Robert M. Mason ◽  
John W. Williams ◽  
Paul Ryl
Keyword(s):  
Interval Estimates
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