Constructing a confidence interval for the ratio of normal distribution quantiles

In 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.

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

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%.

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

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.