Confidence Intervals for the Ratio of the Coefficients of Variation of Inverse-Gamma Distributions

2021 ◽  
Author(s):  
Theerapong Kaewprasert ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Intervals ◽  
Bayesian Method ◽  
Simulation Studies ◽  
Jeffreys Prior ◽  
Inverse Gamma ◽  
Gamma Distributions ◽  
Coefficients Of Variation ◽  
Coverage Probabilities ◽  
Percentile Bootstrap ◽  
Better Than

Herein, we present four methods for constructing confidence intervals for the ratio of the coefficients of variation of inverse-gamma distributions using the percentile bootstrap, fiducial quantities, and Bayesian methods based on the Jeffreys and uniform priors. We compared their performances using coverage probabilities and expected lengths via simulation studies. The results show that the confidence intervals constructed with the Bayesian method based on the uniform prior and fiducial quantities performed better than those constructed with the Bayesian method based on the Jeffreys prior and the percentile bootstrap. Rainfall data from Thailand was used to illustrate the efficacies of the proposed methods.

scholarly journals The Bayesian confidence intervals for measuring the difference between dispersions of rainfall in Thailand

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e9662
Author(s):  
Noppadon Yosboonruang ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Rainfall Data ◽  
Posterior Density ◽  
Lognormal Distributions ◽  
Coefficients Of Variation ◽  
Coverage Probabilities ◽  
The Difference ◽  
Fiducial Generalized Confidence Interval ◽  
Highest Posterior Density

The coefficient of variation is often used to illustrate the variability of precipitation. Moreover, the difference of two independent coefficients of variation can describe the dissimilarity of rainfall from two areas or times. Several researches reported that the rainfall data has a delta-lognormal distribution. To estimate the dynamics of precipitation, confidence interval construction is another method of effectively statistical inference for the rainfall data. In this study, we propose confidence intervals for the difference of two independent coefficients of variation for two delta-lognormal distributions using the concept that include the fiducial generalized confidence interval, the Bayesian methods, and the standard bootstrap. The performance of the proposed methods was gauged in terms of the coverage probabilities and the expected lengths via Monte Carlo simulations. Simulation studies shown that the highest posterior density Bayesian using the Jeffreys’ Rule prior outperformed other methods in virtually cases except for the cases of large variance, for which the standard bootstrap was the best. The rainfall series from Songkhla, Thailand are used to illustrate the proposed confidence intervals.

scholarly journals Evaluation of Bootstrap Confidence Intervals Using a New Non-Normal Process Capability Index

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 484 ◽  
Author(s):  
Gadde Srinivasa Rao ◽  
Mohammed Albassam ◽  
Muhammad Aslam
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Process Capability ◽  
Real Data ◽  
Process Capability Index ◽  
Monte Carlo Simulation Study ◽  
Bootstrap Confidence Intervals ◽  
Capability Index ◽  
Coverage Probabilities ◽  
Percentile Bootstrap

This paper assesses the bootstrap confidence intervals of a newly proposed process capability index (PCI) for Weibull distribution, using the logarithm of the analyzed data. These methods can be applied when the quality of interest has non-symmetrical distribution. Bootstrap confidence intervals, which consist of standard bootstrap (SB), percentile bootstrap (PB), and bias-corrected percentile bootstrap (BCPB) confidence interval are constructed for the proposed method. A Monte Carlo simulation study is used to determine the efficiency of newly proposed index Cpkw over the existing method by addressing the coverage probabilities and average widths. The outcome shows that the BCPB confidence interval is recommended. The methodology of the proposed index has been explained by using the real data of breaking stress of carbon fibers.

scholarly journals Confidence Intervals for Assessing Non-Inferiority with Assay Sensitivity in a Three-Arm Trial with Normally Distributed Endpoints

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 167
Author(s):  
Niansheng Tang ◽  
Fan Liang
Keyword(s):  
Hypothesis Test ◽  
Parametric Bootstrap ◽  
Simulation Studies ◽  
Assay Sensitivity ◽  
Coverage Probabilities ◽  
Empirical Coverage ◽  
Fiducial Method ◽  
Work Done ◽  
Better Than ◽  
Normally Distributed

Various approaches including hypothesis test and confidence interval (CI) construction have been proposed to assess non-inferiority and assay sensitivity via a known fraction or pre-specified margin in three-arm trials with continuous or discrete endpoints. However, there is little work done on the construction of the non-inferiority margin from historical data and simultaneous generalized CIs (SGCIs) in a three-arm trial with the normally distributed endpoints. Based on the generalized fiducial method and the square-and-add method, we propose two simultaneous CIs for assessing non-inferiority and assay sensitivity in a three-arm trial. For comparison, we also consider the Wald-type Bonferroni simultaneous CI and parametric bootstrap simultaneous CI. An algorithm for evaluating the optimal sample size for attaining the pre-specified power is given. Simulation studies are conducted to investigate the performance of the proposed CIs in terms of their empirical coverage probabilities. An example taken from the mildly asthmatic study is illustrated using the proposed simultaneous CIs. Empirical results show that the proposed generalized fiducial method and the square-and-add method behave better than other two compared CIs.

Confidence Intervals After Variance Stabilization May Go Head-to-Head with Exact Confidence Intervals: A New Class of Illustrations

2021 ◽  
pp. 000806832110511
Author(s):  
Nitis Mukhopadhyay
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Large Sample ◽  
New Class ◽  
Variance Stabilization ◽  
Subject Classifications ◽  
Coverage Probabilities ◽  
Exact Confidence Intervals ◽  
Exact Calculations ◽  
Better Than

We begin with an overview on variance stabilizing transformations (VST) along with three classical examples for completeness: the arcsine, square-root and Fisher's z-transformations (Examples 1–3). Then, we construct three new examples (Examples 4–6) of VST-based and central limit theorem (CLT)’based large-sample confidence interval methodologies. These are special examples in the sense that in each situation, we also have an exact confidence interval procedure for the parameter of interest. Tables 1–3 obtained exclusively under Examples 4–6 via exact calculations show that the VST-based (a) large-sample confidence interval methodology wins over the CLT-based large-sample confidence interval methodology, (b) confidence intervals’ exact coverage probabilities are better than or nearly same as those associated with the exact confidence intervals and (c) intervals are never wider (in the log-scale) than the CLT-based intervals across the board. A possibility of such a surprising behaviour of the VST-based confidence intervals over the exact intervals was not on our radar when we began this investigation. Indeed the VST-based inference methodologies may do extremely well, much more so than the existing literature reveals as evidenced by the new Examples 4–6. AMS subject classifications: 62E20; 62F25; 62F12

Combining two soil property rasters using an adaptive gating approach

Soil Research ◽  
2015 ◽  
Vol 53 (8) ◽  
pp. 907 ◽  
Author(s):  
David Clifford ◽  
Yi Guo
Keyword(s):  
Confidence Intervals ◽  
Soil Property ◽  
Mean Squared Error ◽  
Geographic Space ◽  
Covariate Information ◽  
Squared Error ◽  
Inverse Variance ◽  
Machine Learning Approach ◽  
Further Development ◽  
Better Than

Given the wide variety of ways one can measure and record soil properties, it is not uncommon to have multiple overlapping predictive maps for a particular soil property. One is then faced with the challenge of choosing the best prediction at a particular point, either by selecting one of the maps, or by combining them together in some optimal manner. This question was recently examined in detail when Malone et al. (2014) compared four different methods for combining a digital soil mapping product with a disaggregation product based on legacy data. These authors also examined the issue of how to compute confidence intervals for the resulting map based on confidence intervals associated with the original input products. In this paper, we propose a new method to combine models called adaptive gating, which is inspired by the use of gating functions in mixture of experts, a machine learning approach to forming hierarchical classifiers. We compare it here with two standard approaches – inverse-variance weights and a regression based approach. One of the benefits of the adaptive gating approach is that it allows weights to vary based on covariate information or across geographic space. As such, this presents a method that explicitly takes full advantage of the spatial nature of the maps we are trying to blend. We also suggest a conservative method for combining confidence intervals. We show that the root mean-squared error of predictions from the adaptive gating approach is similar to that of other standard approaches under cross-validation. However under independent validation the adaptive gating approach works better than the alternatives and as such it warrants further study in other areas of application and further development to reduce its computational complexity.

scholarly journals On Genetic Map Functions

Genetics ◽  
1996 ◽  
Vol 142 (4) ◽  
pp. 1369-1377
Author(s):  
Hongyu Zhao ◽  
Terence P Speed
Keyword(s):  
Genetic Distance ◽  
Genetic Map ◽  
Probability Model ◽  
Recombination Fraction ◽  
Renewal Processes ◽  
Gamma Distributions ◽  
Multilocus Analysis ◽  
Map Function ◽  
Better Than

Abstract Various genetic map functions have been proposed to infer the unobservable genetic distance between two loci from the observable recombination fraction between them. Some map functions were found to fit data better than others. When there are more than three markers, multilocus recombination probabilities cannot be uniquely determined by the defining property of map functions, and different methods have been proposed to permit the use of map functions to analyze multilocus data. If for a given map function, there is a probability model for recombination that can give rise to it, then joint recombination probabilities can be deduced from this model. This provides another way to use map functions in multilocus analysis. In this paper we show that stationary renewal processes give rise to most of the map functions in the literature. Furthermore, we show that the interevent distributions of these renewal processes can all be approximated quite well by gamma distributions.

scholarly journals Coverage versus Confidence

2021 ◽  
Vol 23 ◽  
Author(s):  
Peyton Cook
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Coverage Probability ◽  
Negative Binomial ◽  
Asymptotic Confidence Interval ◽  
Population Proportion ◽  
Coverage Probabilities ◽  
The Mean

This article is intended to help students understand the concept of a coverage probability involving confidence intervals. Mathematica is used as a language for describing an algorithm to compute the coverage probability for a simple confidence interval based on the binomial distribution. Then, higher-level functions are used to compute probabilities of expressions in order to obtain coverage probabilities. Several examples are presented: two confidence intervals for a population proportion based on the binomial distribution, an asymptotic confidence interval for the mean of the Poisson distribution, and an asymptotic confidence interval for a population proportion based on the negative binomial distribution.

scholarly journals Volatility filtering in estimation of kurtosis (and variance)

2019 ◽  
Vol 7 (1) ◽  
pp. 1-23
Author(s):  
Stanislav Anatolyev
Keyword(s):  
Confidence Intervals ◽  
Method Of Moments ◽  
Usual Method ◽  
Coverage Probabilities ◽  
High Volatility ◽  
Filtering Technique ◽  
The One ◽  
Moments Estimates ◽  
Thick Tails ◽  
Kurtosis Coefficient

AbstractThe kurtosis of the distribution of financial returns characterized by high volatility persistence and thick tails is notoriously difficult to estimate precisely. We propose a simple but effective procedure of estimating the kurtosis coefficient (and variance) based on volatility filtering that uses a simple GARCH model. In addition to an estimate, the proposed algorithm issues a signal of whether the kurtosis (or variance) is finite or infinite. We also show how to construct confidence intervals around the proposed estimates. Simulations indicate that the proposed estimates are much less median biased than the usual method-of-moments estimates, their confidence intervals having much more precise coverage probabilities. The procedure alsoworks well when the underlying volatility process is not the one the filtering technique is based on. We illustrate how the algorithm works using several actual series of returns.

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