scholarly journals Confidence Intervals for the Coefficient of Quartile Variation of a Zero-inflated Lognormal Distribution

2021 ◽  
Vol 5 (4) ◽  
pp. 457-470
Author(s):  
Noppadon Yosboonruang ◽  
Sa-Aat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Lognormal Distribution ◽  
Real Data ◽  
Skewed Distribution ◽  
Trawl Survey ◽  
Statistical Tool ◽  
Generalized Confidence Interval ◽  
Chi Squared ◽  
Credible Intervals ◽  
Fiducial Generalized Confidence Interval

There are many types of skewed distribution, one of which is the lognormal distribution that is positively skewed and may contain true zero values. The coefficient of quartile variation is a statistical tool used to measure the dispersion of skewed and kurtosis data. The purpose of this study is to establish confidence and credible intervals for the coefficient of quartile variation of a zero-inflated lognormal distribution. The proposed approaches are based on the concepts of the fiducial generalized confidence interval, and the Bayesian method. Coverage probabilities and expected lengths were used to evaluate the performance of the proposed approaches via Monte Carlo simulation. The results of the simulation studies show that the fiducial generalized confidence interval and the Bayesian based on uniform and normal inverse Chi-squared priors were appropriate in terms of the coverage probability and expected length, while the Bayesian approach based on Jeffreys' rule prior can be used as alternatives. In addition, real data based on the red cod density from a trawl survey in New Zealand is used to illustrate the performances of the proposed approaches. Doi: 10.28991/esj-2021-01289 Full Text: PDF

scholarly journals Measuring the dispersion of rainfall using Bayesian confidence intervals for coefficient of variation of delta-lognormal distribution: a study from Thailand

PeerJ ◽  
2019 ◽  
Vol 7 ◽  
pp. e7344 ◽  
Author(s):  
Noppadon Yosboonruang ◽  
Sa-aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Bayesian Methods ◽  
Coefficient Of Variation ◽  
Lognormal Distribution ◽  
Real Life ◽  
Rainfall Data ◽  
Data Series ◽  
Fiducial Generalized Confidence Interval ◽  
Highest Posterior Density

Since rainfall data series often contain zero values and thus follow a delta-lognormal distribution, the coefficient of variation is often used to illustrate the dispersion of rainfall in a number of areas and so is an important tool in statistical inference for a rainfall data series. Therefore, the aim in this paper is to establish new confidence intervals for a single coefficient of variation for delta-lognormal distributions using Bayesian methods based on the independent Jeffreys’, the Jeffreys’ Rule, and the uniform priors compared with the fiducial generalized confidence interval. The Bayesian methods are constructed with either equitailed confidence intervals or the highest posterior density interval. The performance of the proposed confidence intervals was evaluated using coverage probabilities and expected lengths via Monte Carlo simulations. The results indicate that the Bayesian equitailed confidence interval based on the independent Jeffreys’ prior outperformed the other methods. Rainfall data recorded in national parks in July 2015 and in precipitation stations in August 2018 in Nan province, Thailand are used to illustrate the efficacy of the proposed methods using a real-life dataset.

Generalized confidence interval for an agreement between raters

2021 ◽  
Vol 40 (9) ◽  
pp. 2230-2238
Author(s):  
Dulal K. Bhaumik ◽  
Hairong Shi ◽  
Domenic J. Reda ◽  
Bikas K. Sinha
Keyword(s):  
Confidence Interval ◽  
Generalized Confidence Interval

scholarly journals Inference of stress-strength reliability for two-parameter of exponentiated Gumbel distribution based on lower record values

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0249028
Author(s):  
Ehsan Fayyazishishavan ◽  
Serpil Kılıç Depren
Keyword(s):  
Information Matrix ◽  
Gumbel Distribution ◽  
Sampling Technique ◽  
Real Data ◽  
Record Values ◽  
Unknown Parameters ◽  
Data Set ◽  
Credible Intervals ◽  
Lower Records ◽  
Two Parameter

The two-parameter of exponentiated Gumbel distribution is an important lifetime distribution in survival analysis. This paper investigates the estimation of the parameters of this distribution by using lower records values. The maximum likelihood estimator (MLE) procedure of the parameters is considered, and the Fisher information matrix of the unknown parameters is used to construct asymptotic confidence intervals. Bayes estimator of the parameters and the corresponding credible intervals are obtained by using the Gibbs sampling technique. Two real data set is provided to illustrate the proposed methods.

scholarly journals Inferences for Weibull parameters under progressively first-failure censored data with binomial random removals

2020 ◽  
Vol 9 (1) ◽  
pp. 47-60
Author(s):  
Samir K. Ashour ◽  
Ahmed A. El-Sheikh ◽  
Ahmed Elshahhat
Keyword(s):  
Monte Carlo ◽  
Censored Data ◽  
Real Data ◽  
Unknown Parameters ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Squared Error Loss Function ◽  
Bayes Estimates ◽  
Monte Carlo Techniques ◽  
Credible Intervals

In this paper, the Bayesian and non-Bayesian estimation of a two-parameter Weibull lifetime model in presence of progressive first-failure censored data with binomial random removals are considered. Based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimators, two-sided approximate confidence intervals for the unknown parameters are constructed. Using gamma conjugate priors, several Bayes estimates and associated credible intervals are obtained relative to the squared error loss function. Proposed estimators cannot be expressed in closed forms and can be evaluated numerically by some suitable iterative procedure. A Bayesian approach is developed using Markov chain Monte Carlo techniques to generate samples from the posterior distributions and in turn computing the Bayes estimates and associated credible intervals. To analyze the performance of the proposed estimators, a Monte Carlo simulation study is conducted. Finally, a real data set is discussed for illustration purposes.

Reasons of unsuccessful implantation of short-term hemodialysis catheters in jugular veins using real-time ultrasound

2018 ◽  
Vol 19 (5) ◽  
pp. 467-472
Author(s):  
Mauro Sergio Martins Marrocos ◽  
Thais Marques S Gentil ◽  
Fernanda de C Lima ◽  
Sandra Maria R Laranja
Keyword(s):  
Confidence Interval ◽  
Real Time ◽  
Odds Ratio ◽  
Short Term ◽  
Open Label ◽  
Jugular Veins ◽  
Open Label Study ◽  
Label Study ◽  
Chi Squared ◽  
Internal Jugular Veins

Purpose: Real-time ultrasound is indicated for hemodialysis catheters’ insertion in internal jugular veins. We evaluated unsuccessful implantation of short-term hemodialysis catheters in internal jugular veins using real-time ultrasound between patients with and without previous short-term catheters. Methods: Observational open-label study of unsuccessful implantation of short-term hemodialysis catheters in internal jugular veins using real-time ultrasound from July 2013 to August 2014. Results: A total of 185 procedures were compared in 122 individuals; 120 (64.86%) had previously used short-term catheters. There were 5 (8%) unsuccessful implantation among 62 catheterizations without previous short-term catheter and 41 (33.6%) among 122 with previous short-term catheter (p = 0.001 Pearson’s chi-squared, odds ratio = 5.77, 95% confidence interval = 2.15–15.50, p = 0.001). Non-progressing guidewire occurred in 2 (3.2%) of 62 patients without previous short-term catheter and in 18 (14.8%) of 122 with previous short-term catheter (p = 0.018 Pearson’s chi-squared, odds ratio = 5.19, 95% confidence interval = 1.16–23.15, p = 0.031). No difference was observed between size of the veins with or without non-progressing guidewire. All 11 cases of venous thrombosis occurred in patients who had previous short-term catheter removed due to infection. Conclusion: Previous use of short-term catheter is pivotal in the occurrence of unsuccessful implantation of short-term catheter in internal jugular veins using real-time ultrasound.

scholarly journals Measures of the Degree of Departure from Ignorable Sample Selection

2019 ◽  
Vol 8 (5) ◽  
pp. 932-964 ◽  
Author(s):  
Roderick J A Little ◽  
Brady T West ◽  
Philip S Boonstra ◽  
Jingwei Hu
Keyword(s):  
Sample Selection ◽  
Real Data ◽  
Sampling Bias ◽  
Inclusion Probability ◽  
Probability Sampling ◽  
Simple Index ◽  
Central Value ◽  
Credible Intervals ◽  
Standardized Measure ◽  
Fully Bayesian

Abstract With the current focus of survey researchers on “big data” that are not selected by probability sampling, measures of the degree of potential sampling bias arising from this nonrandom selection are sorely needed. Existing indices of this degree of departure from probability sampling, like the R-indicator, are based on functions of the propensity of inclusion in the sample, estimated by modeling the inclusion probability as a function of auxiliary variables. These methods are agnostic about the relationship between the inclusion probability and survey outcomes, which is a crucial feature of the problem. We propose a simple index of degree of departure from ignorable sample selection that corrects this deficiency, which we call the standardized measure of unadjusted bias (SMUB). The index is based on normal pattern-mixture models for nonresponse applied to this sample selection problem and is grounded in the model-based framework of nonignorable selection first proposed in the context of nonresponse by Don Rubin in 1976. The index depends on an inestimable parameter that measures the deviation from selection at random, which ranges between the values zero and one. We propose the use of a central value of this parameter, 0.5, for computing a point index, and computing the values of SMUB at zero and one to provide a range of the index in a sensitivity analysis. We also provide a fully Bayesian approach for computing credible intervals for the SMUB, reflecting uncertainty in the values of all of the input parameters. The proposed methods have been implemented in R and are illustrated using real data from the National Survey of Family Growth.

Common risk difference test and interval estimation of risk difference for stratified bilateral correlated data

2018 ◽  
Vol 28 (8) ◽  
pp. 2418-2438
Author(s):  
Xi Shen ◽  
Chang-Xing Ma ◽  
Kam C Yuen ◽  
Guo-Liang Tian
Keyword(s):  
Data Analysis ◽  
Confidence Interval ◽  
Score Test ◽  
Real Data ◽  
Risk Difference ◽  
Error Rates ◽  
Correlated Data ◽  
Test Statistic ◽  
Data Set ◽  
Intra Class Correlation

Bilateral correlated data are often encountered in medical researches such as ophthalmologic (or otolaryngologic) studies, in which each unit contributes information from paired organs to the data analysis, and the measurements from such paired organs are generally highly correlated. Various statistical methods have been developed to tackle intra-class correlation on bilateral correlated data analysis. In practice, it is very important to adjust the effect of confounder on statistical inferences, since either ignoring the intra-class correlation or confounding effect may lead to biased results. In this article, we propose three approaches for testing common risk difference for stratified bilateral correlated data under the assumption of equal correlation. Five confidence intervals of common difference of two proportions are derived. The performance of the proposed test methods and confidence interval estimations is evaluated by Monte Carlo simulations. The simulation results show that the score test statistic outperforms other statistics in the sense that the former has robust type [Formula: see text] error rates with high powers. The score confidence interval induced from the score test statistic performs satisfactorily in terms of coverage probabilities with reasonable interval widths. A real data set from an otolaryngologic study is used to illustrate the proposed methodologies.

scholarly journals Estimation of Generalized Gompertz Distribution Parameters under Ranked-Set Sampling

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Mohammed Obeidat ◽  
Amjad Al-Nasser ◽  
Amer I. Al-Omari
Keyword(s):  
Monte Carlo ◽  
Real Data ◽  
Small Samples ◽  
Simple Random Sample ◽  
Unknown Parameters ◽  
Bayesian Approaches ◽  
Bayes Estimates ◽  
Gompertz Distribution ◽  
Distribution Parameters ◽  
Credible Intervals

This paper studies estimation of the parameters of the generalized Gompertz distribution based on ranked-set sample (RSS). Maximum likelihood (ML) and Bayesian approaches are considered. Approximate confidence intervals for the unknown parameters are constructed using both the normal approximation to the asymptotic distribution of the ML estimators and bootstrapping methods. Bayes estimates and credible intervals of the unknown parameters are obtained using differential evolution Markov chain Monte Carlo and Lindley’s methods. The proposed methods are compared via Monte Carlo simulations studies and an example employing real data. The performance of both ML and Bayes estimates is improved under RSS compared with simple random sample (SRS) regardless of the sample size. Bayes estimates outperform the ML estimates for small samples, while it is the other way around for moderate and large samples.

scholarly journals Propositions for Confidence Interval in Systematic Sampling on Real Line

2016 ◽  
Author(s):  
Mehmet Niyazi Çankaya
Keyword(s):  
Confidence Interval ◽  
Real Line ◽  
Variance Estimation ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Real Data ◽  
Systematic Sampling ◽  
Radiological Images ◽  
Quantitative Results ◽  
Dimensional Object

The systematic sampling is used as a method to get the quantitative results from the tissues and the radiological images. Systematic sampling on real line (R) is a very attractive method within which the biomedical imaging is consulted by the practitioners. For the systematic sampling on R, the measurement function (MF) is occurred by slicing the three dimensional object equidistant  systematically. If the parameter q of MF is estimated to be small enough for mean square error, we can make the important remarks for the design-based stereology. This study is an extension of [17], and an exact calculation method is proposed to calculate the constant λ(q,N) of confidence interval in the systematic sampling. In the results, synthetic data can support the results of real data. The currently used covariogram model in variance approximation proposed by [28,29] is tested for the different measurement functions to see the performance on the variance estimation of systematically sampled R. The exact value of constant λ(q,N) is examined for the different measurement functions as well.

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