Article
Mathematical & Computational Biology
Lonnie Turpin, Jeanne-Claire Patin, William Jens, Morgan Turpin
Summary: This study develops two functions (one for each level) that provide approximations of the exact lower-bound L within a/a3 when considering the one-sided binomial confidence interval (L , 1) containing the unknown parameter p. The exponential and logarithmic functions are found to outperform the standard rule of three L ? 1- 3/n over their respective ranges, covering all sample sizes n = 1. Specifically, the exponential function with exp(-3/n) is a better lower bound when a = 0.05 and n < 1054, while exp(-4.6569/n) is a better bound when a = 0.01 and n < 209.
INTERNATIONAL JOURNAL OF BIOSTATISTICS
(2023)
Article
Statistics & Probability
Angkana Kokaew, Winai Bodhisuwan, Su-Fen Yang, Andrei Volodin
Summary: This article investigates the logarithmic interval estimation of a ratio of two binomial proportions in dependent samples. The study finds that closed-form solutions to confidence intervals for the difference and ratio of correlated proportions are typically not available and the computation process is complex. Through a Monte Carlo simulation, we demonstrate the reliability of using a normal approximation for the estimation of the ratio and provide recommendations for the asymptotic logarithmic interval.
JOURNAL OF APPLIED STATISTICS
(2023)
Article
Multidisciplinary Sciences
Lorentz Jantschi
Summary: This paper discusses the challenge of mathematically evaluating the exact confidence interval for sampled outcomes, which follow a binomial distribution. It proposes three alternative methods for calculating confidence intervals and provides descriptions and examples for each.
Article
Statistics & Probability
Chanakan Sungboonchoo, Su-Fen Yang, Wararit Panichkitkosolkul, Andrei Volodin
Summary: We investigated the problem of logarithmic interval estimation for a cross-product ratio with data from two independent Bernoulli samples. Asymptotic logarithmic confidence intervals were constructed under different types of sampling schemes, and the parameter estimators showed exponentially decreasing bias. Our findings suggest that the relatively simple normal approximations are reliable for constructing logarithmic confidence intervals.
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
(2023)
Article
Statistics & Probability
Junsik Kim, Woncheol Jang
Summary: This paper explores the construction of confidence intervals for a binomial proportion p, proposing a generalized Agresti-Coull type confidence interval by adjusting bias with the saddlepoint approximation. The coverage probabilities and lengths of the proposed interval are compared to other popular asymptotic confidence intervals, showing it to be more stable at the boundaries of p compared to the Wilson interval, and having a shorter length than the Agresti-Coull interval.
JOURNAL OF THE KOREAN STATISTICAL SOCIETY
(2022)
Article
Mathematics
Felix Almendra-Arao, Hortensia Reyes-Cervantes, Marcos Morales-Cortes
Summary: Confidence intervals are important tools for estimating binomial proportions in statistics, with the most well-known being the Wald and Clopper-Pearson intervals. However, these intervals are known to have shortcomings in terms of coverage probability and expected mean length, leading to the proposal of alternative intervals. In this study, we investigate the performance of several of these confidence intervals using a parametric family to estimate the parameter p. Instead of using the confidence intervals approach, our analysis is done through hypothesis tests. Our main goal is to identify values of c that yield better-performing tests and establish an optimal procedure.
Article
Mathematics
Lorentz Jantschi
Summary: Medical studies often compare two outcomes from samples, with the importance placed on the probability and confidence in the findings. Current guidelines recommend reporting both relative and absolute measures of association, but the exact confidence interval for these measures poses a mathematical challenge due to the discrete distribution. In order to address this issue, algorithms implementing a strategy for providing exact p-values and confidence intervals have been proposed.
Article
Computer Science, Theory & Methods
Dong Qiu
Summary: The paper demonstrates that the generalized Hukuhara differentiability of interval-valued function at a point is not fully equivalent to the one-sided differentiability of its endpoint functions through a counterexample, and then presents a complete characterization of the generalized Hukuhara differentiability of interval-valued functions. The results include existing cases in the literature and new cases where functions are gH-differentiable at a point but not continuous in any deleted neighborhood of that point.
FUZZY SETS AND SYSTEMS
(2021)
Article
Computer Science, Interdisciplinary Applications
Chung-Han Lee, Hsiuying Wang
Summary: This study proposes an approach to construct confidence intervals for the proportion of conformance and provides a methodology to calculate the exact confidence coefficients of the proposed intervals. Numerical and simulation studies are conducted to compare the performance of these intervals.
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
(2021)
Article
Medicine, General & Internal
Mohamad Adam Bujang
Summary: Sample size calculation based on a specified width of 95% confidence interval allows researchers to determine the level of statistical accuracy they want to achieve for a study. This paper provides a conceptual background for sensitivity and specificity analysis and presents sample size tables based on a 95% confidence interval width. The paper also offers recommendations for sample size planning in diagnostic and screening scenarios, as well as discusses other relevant considerations in determining the minimum sample size and drafting the sample size statement for sensitivity and specificity analysis.
Article
Mathematics
Carl Johan Casselgren
Summary: This note affirms the existence of a cubic polynomial for X-interval coloring and deduces improved upper bounds for bipartite graphs with small maximum degree. The authors provide a positive answer to the question posed by Casselgren and Toft (2016), demonstrating that the X-interval coloring can be achieved with a polynomial of degree three.
DISCRETE MATHEMATICS
(2022)
Article
Pharmacology & Pharmacy
Kaifeng Lu, Hua Guo
Summary: This passage explores the application of multiple imputation techniques in parameter estimation, comparing the MN method with the LMB method. Through simulation studies, it is found that the proposed method produces slightly shorter confidence intervals compared to the LMB method, while also being evaluable for all datasets.
PHARMACEUTICAL STATISTICS
(2022)
Article
Engineering, Industrial
Zahra Saberzadeh, Mostafa Razmkhah
Summary: The reliability of complex systems consisting of n independent elements, each with two dependent components, is investigated based on degradation data. A copula-based model is used to describe the dependence structure of the components. The reliability of a complex system is derived for different copula functions, considering gamma, Wiener, and inverse Gaussian processes for the degradation of each component. Reliability bounds are obtained by assuming positive association of components for special cases of series and parallel systems. A two-step method is proposed for estimating maximum likelihood estimators when model parameters are unknown. The performance of the estimators is evaluated through a simulation study, and the sensitivity of system reliability is analyzed using simulation. The results of the paper are illustrated using two real examples.
RELIABILITY ENGINEERING & SYSTEM SAFETY
(2022)
Article
Automation & Control Systems
Wei Zheng, Taeho Jung, Hai Lin
Summary: Formulating cyber-security problems with attackers and defenders as a partially observable stochastic game has become a trend recently. This paper focuses on a turn-based one-sided two-player zero-sum partially observable stochastic game (OTZ-POSG) with the assumption of public actions. The existence and properties of a Stackelberg equilibrium for this game are investigated and a space partition approach is proposed to solve the game iteratively.
Article
Engineering, Multidisciplinary
Caleb King, Peter Parker, Derek S. Young
Summary: This paper presents an empirical study that generates robust weights for linear extrapolation, greatly improving the accuracy of coverage in a feasible range of distribution families with positive support.
QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL
(2023)
