Generalized pivotal quantities (GPQs) and generalized confidence intervals (GCIs) have proven to be useful tools for making inferences in many practical problems. Although GCIs are not guaranteed to have exact frequentist coverage, a number of published and unpublished simulation studies suggest that the coverage probabilities of such intervals are sufficiently close to their nominal value so a...

Abstract The purpose of this paper is to study and compare the methods for constructing confidence intervals variance components in an unbalanced one-way random effects model. are based on a classical exact, generalised pivotal quantity, fiducial inference quantity. comparison criteria involves empirical coverage probability that maintains at nominal level 0.95 shortest average length interval....

Optimization methods have been widely applied in statistics. Among them, capability measuring techniques are widely applied in industries. Process Capability Indices (PCIs) have been proposed for measuring process production capability. This paper concentrates, the lower and upper confidence limits for the PCIs are obtained from generalized pivotal quantity of random model and also, use this co...

This research considers several log-normal distributions when variances are heteroscedastic and group sizes are unequal. We proposed fiducial generalized pivotal quantities (FGPQ)-based simultaneous confidence intervals for ratios of the means. We also proved that the constructed confidence intervals have correct asymptotic coverage. Simulation results show that the proposed methods work well. ...

Abstract: In this paper we extend Fisher’s fiducial argument and obtain a generalized fiducial recipe that greatly expands the applicability of fiducial ideas. We do this assuming as little structure as possible. We demonstrate this recipe on many examples of varying complexity. We investigate, by simulation and by theoretical considerations, some properties of the statistical procedures derive...

Generalized Confidence Intervals (GCI) can be constructed for cases where an exact confidence interval based on sufficient statistics is not available. In this thesis, we first review three existing tests for log-normal data using the GCI approach. Then we propose fiducial generalized pivotal quantities (FGPQ)-based simultaneous confidence intervals for ratios of log-normal means, and prove tha...

For binary outcome data from epidemiological studies, this article investigates the interval estimation of several measures of interest in the absence or presence of categorical covariates. When covariates are present, the logistic regression model as well as the log-binomial model are investigated. The measures considered include the common odds ratio (OR) from several studies, the number need...

One aspect of Fisher’s work which has puzzled a great many statisticians is the idea of Fiducial Inference. Using “pivotal” variables, Fisher moves from logical statements about restrictions of parameter spaces to probabilistic statements about parameters. The method works, but with a lot of caveats: the pivotal variables must be sufficient statistics, must be continuous, &c. Dempster’s explora...