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The Semi-Hyperbolic Distribution and Its Applications 半双曲分布及其应用
Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-21 DOI: 10.3390/stats6040071
Roman V. Ivanov
This paper studies a subclass of the class of generalized hyperbolic distribution called the semi-hyperbolic distribution. We obtain analytical expressions for the cumulative distribution function and, specifically, their first and second lower partial moments. Using the received formulas, we compute the value at risk, the expected shortfall, and the semivariance in the semi-hyperbolic model of the financial market. The formulas depend on the values of generalized hypergeometric functions and modified Bessel functions of the second kind. The research illustrates the possibility of analysis of generalized hyperbolic models using the same methodology as is employed for the well-established variance-gamma model.
本文研究了广义双曲分布类的一个子类——半双曲分布。我们得到了累积分布函数的解析表达式,特别是它们的一阶和二阶下偏矩。利用所得到的公式,我们计算了金融市场半双曲模型中的风险值、预期缺口和半方差。这些公式依赖于广义超几何函数和第二类修正贝塞尔函数的值。该研究说明了使用与已建立的方差-伽马模型相同的方法分析广义双曲模型的可能性。
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引用次数: 0
An Archimedean Copulas-Based Approach for m-Consecutive-k-Out-of-n: F Systems with Exchangeable Components 具有可交换分量的m-连续-k- of-n: F系统的阿基米德copulas方法
Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-20 DOI: 10.3390/stats6040070
Ioannis S. Triantafyllou
It is evident that several real-life applications, such as telecommunication systems, call for the establishment of consecutive-type networks. Moreover, some of them require more complex connectors than the ones that exist already in the literature. Thereof, in the present work we provide a signature-based study of a reliability network consisting of identical m-consecutive-k-out-of-n: F structures with exchangeable components. The dependency of the components of each system is modeled with the aid of well-known Archimedean copulas. Exact formulae for determining the expected lifetime of the underlying reliability scheme are provided under different Archimedean copulas-based assumptions. Several numerical results are carried out to shed light on the performance of the resulting consecutive-type design. Some thoughts on extending the present study to more complex consecutive-type reliability structures are also discussed.
显然,一些实际应用,例如电信系统,要求建立连续型网络。此外,它们中的一些需要比现有文献中存在的连接器更复杂的连接器。因此,在目前的工作中,我们提供了一个基于签名的可靠性网络的研究,该网络由具有可交换组件的相同m-连续k- of-n: F结构组成。每个系统的组件的依赖关系是借助著名的阿基米德copulas建模的。在不同的基于阿基米德耦合的假设下,给出了确定基础可靠性方案预期寿命的精确公式。几个数值结果进行了阐明所得到的连续型设计的性能。讨论了将本研究扩展到更复杂的连续型可靠度结构的一些想法。
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引用次数: 0
Exploring the Consumer Acceptance of Nano Clothing Using a PLS-SEM Analysis 利用PLS-SEM分析探索消费者对纳米服装的接受程度
Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-19 DOI: 10.3390/stats6040069
Andreea-Ionela Puiu, Rodica Ianole-Călin, Elena Druică
We use an extended framework of the technology acceptance model (TAM) to identify the most significant drivers behind the intention to buy clothes produced with nano fabrics (nano clothing). Based on survey data, we estimate an integrated model that explains this intention as being driven by attitudes, perceived usefulness, and perceived ease of use. The influences of social innovativeness, relative advantage, compatibility, and ecologic concern on perceived usefulness are tested using perceived ease of use as a mediator. We employ a partial least squares path model in WarpPLS 7.0., a predictive technique that informs policies. The results show positive effects for all the studied relationships, with effect sizes underscoring perceived usefulness, attitude, and compatibility as the most suitable targets for practical interventions. Our study expands the TAM framework into the field of nano fashion consumption, shedding light on the potential drivers of the adoption process. Explorations of the topic hold the potential to make a substantial contribution to the promotion of sustainable fashion practices.
我们使用技术接受模型(TAM)的扩展框架来确定购买用纳米织物生产的衣服(纳米服装)意图背后最重要的驱动因素。根据调查数据,我们估计了一个综合模型,该模型解释了这种意图是由态度、感知有用性和感知易用性驱动的。以感知易用性为中介,考察社会创新性、相对优势、兼容性和生态关注对感知有用性的影响。我们在WarpPLS 7.0中采用了偏最小二乘路径模型。,一种为政策提供信息的预测技术。结果显示,所有研究的关系都有积极的影响,效应量强调感知有用性、态度和兼容性是实际干预最合适的目标。我们的研究将TAM框架扩展到纳米时尚消费领域,揭示了采用过程的潜在驱动因素。对这一主题的探索有可能为促进可持续时尚实践做出重大贡献。
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引用次数: 0
Comparison between Two Algorithms for Computing the Weighted Generalized Affinity Coefficient in the Case of Interval Data 区间数据加权广义关联系数两种计算算法的比较
Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-13 DOI: 10.3390/stats6040068
Áurea Sousa, Osvaldo Silva, Leonor Bacelar-Nicolau, João Cabral, Helena Bacelar-Nicolau
From the affinity coefficient between two discrete probability distributions proposed by Matusita, Bacelar-Nicolau introduced the affinity coefficient in a cluster analysis context and extended it to different types of data, including for the case of complex and heterogeneous data within the scope of symbolic data analysis (SDA). In this study, we refer to the most significant partitions obtained using the hierarchical cluster analysis (h.c.a.) of two well-known datasets that were taken from the literature on complex (symbolic) data analysis. h.c.a. is based on the weighted generalized affinity coefficient for the case of interval data and on probabilistic aggregation criteria from a VL parametric family. To calculate the values of this coefficient, two alternative algorithms were used and compared. Both algorithms were able to detect clusters of macrodata (aggregated data into groups of interest) that were consistent and consonant with those reported in the literature, but one performed better than the other in some specific cases. Moreover, both approaches allow for the treatment of large microdatabases (non-aggregated data) after their transformation into macrodata from the huge microdata.
Bacelar-Nicolau从Matusita提出的两个离散概率分布之间的亲和系数出发,将亲和系数引入到聚类分析环境中,并将其扩展到不同类型的数据,包括符号数据分析(SDA)范围内的复杂和异构数据。在本研究中,我们参考了使用层次聚类分析(h.c.a.)从复杂(符号)数据分析文献中获取的两个知名数据集获得的最显著分区。该方法基于区间数据的加权广义亲和系数和VL参数族的概率聚合准则。为了计算该系数的值,使用了两种替代算法并进行了比较。这两种算法都能够检测与文献中报道的一致和一致的宏观数据簇(将数据聚合到感兴趣的组中),但在某些特定情况下,一种算法比另一种算法表现得更好。此外,这两种方法都允许将大型微数据库(非聚合数据)从庞大的微数据转换为宏数据后进行处理。
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引用次数: 1
On the Vector Representation of Characteristic Functions 关于特征函数的向量表示
Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-10 DOI: 10.3390/stats6040067
Wolf-Dieter Richter
Based upon the vector representation of complex numbers and the vector exponential function, we introduce the vector representation of characteristic functions and consider some of its elementary properties such as its polar representation and a vector power expansion.
在复数的向量表示和向量指数函数的基础上,我们引入了特征函数的向量表示,并考虑了它的一些基本性质,如极坐标表示和向量幂展开式。
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引用次数: 0
Newcomb–Benford’s Law in Neuromuscular Transmission: Validation in Hyperkalemic Conditions 神经肌肉传递中的Newcomb-Benford定律:在高钾血症条件下的验证
Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-09 DOI: 10.3390/stats6040066
Adriano Silva, Sergio Floquet, Ricardo Lima
Recently, we demonstrated the validity of the anomalous numbers law, known as Newcomb–Benford’s law, in mammalian neuromuscular transmission, considering different extracellular calcium. The present work continues to examine how changes in extracellular physiological artificial solution can modulate the first digit law in the context of spontaneous acetylcholine release at the neuromuscular junction. Using intracellular measurements, we investigated if the intervals of miniature potentials collected at the neuromuscular junction obey the law in a hyperkalemic environment. When bathed in standard Ringer’s solution, the experiments provided 22,582 intervals extracted from 14 recordings. On the other hand, 690,385 intervals were obtained from 12 experiments in a modified Ringer’s solution containing a high potassium concentration. The analysis showed that the intervals, harvested from recordings at high potassium, satisfactorily obeyed Newcomb–Benford’s law. Furthermore, our data allowed us to uncover a conformity fluctuation as a function of the number of intervals of the miniature potentials. Finally, we discuss the biophysical implications of the present findings.
最近,我们证明了反常数字定律的有效性,即Newcomb-Benford定律,在哺乳动物神经肌肉传递中,考虑到不同的细胞外钙。目前的工作继续研究细胞外生理人工溶液的变化如何在神经肌肉交界处自发释放乙酰胆碱的情况下调节第一指规律。利用细胞内测量,我们研究了在高钾环境下,神经肌肉连接处收集的微型电位的间隔是否服从规律。当浸泡在标准林格溶液中时,实验提供了从14个录音中提取的22,582个间隔。另一方面,在含有高钾浓度的改良林格氏溶液中,从12个实验中得到了690,385个区间。分析表明,在高钾条件下记录的间隔,令人满意地符合纽库姆-本福德定律。此外,我们的数据使我们能够揭示作为微型电位间隔数的函数的一致性波动。最后,我们讨论了本研究结果的生物物理意义。
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引用次数: 0
Computationally Efficient Poisson Time-Varying Autoregressive Models through Bayesian Lattice Filters 基于贝叶斯格滤波器的计算高效泊松时变自回归模型
Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-09 DOI: 10.3390/stats6040065
Yuelei Sui, Scott H. Holan, Wen-Hsi Yang
Estimation of time-varying autoregressive models for count-valued time series can be computationally challenging. In this direction, we propose a time-varying Poisson autoregressive (TV-Pois-AR) model that accounts for the changing intensity of the Poisson process. Our approach can capture the latent dynamics of the time series and therefore make superior forecasts. To speed up the estimation of the TV-AR process, our approach uses the Bayesian Lattice Filter. In addition, the No-U-Turn Sampler (NUTS) is used, instead of a random walk Metropolis–Hastings algorithm, to sample intensity-related parameters without a closed-form full conditional distribution. The effectiveness of our approach is evaluated through model-based and empirical simulation studies. Finally, we demonstrate the utility of the proposed model through an example of COVID-19 spread in New York State and an example of US COVID-19 hospitalization data.
对计数时间序列的时变自回归模型的估计在计算上具有挑战性。在这个方向上,我们提出了一个时变泊松自回归(tv -泊松- ar)模型来解释泊松过程的强度变化。我们的方法可以捕捉到时间序列的潜在动态,因此可以做出更好的预测。为了加速TV-AR过程的估计,我们的方法使用贝叶斯点阵滤波器。此外,使用无掉头采样器(NUTS)代替随机游走Metropolis-Hastings算法,对强度相关参数进行采样,不需要封闭形式的全条件分布。我们的方法的有效性通过基于模型和实证模拟研究进行评估。最后,我们通过一个COVID-19在纽约州传播的例子和一个美国COVID-19住院数据的例子来证明所提出模型的实用性。
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引用次数: 0
Effective Sample Size with the Bivariate Gaussian Common Component Model 二元高斯共分量模型的有效样本量
Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-08 DOI: 10.3390/stats6040064
Letícia Ellen Dal Canton, Luciana Pagliosa Carvalho Guedes, Miguel Angel Uribe-Opazo, Tamara Cantu Maltauro
Effective sample size (ESS) consists of an equivalent number of sampling units of a georeferenced variable that would produce the same sampling error, as it considers the information that each georeferenced sampling unit contains about itself as well as in relation to its neighboring sampling units. This measure can provide useful information in the planning of future georeferenced sampling for spatial variability experiments. The objective of this article was to develop a bivariate methodology for ESS (ESSbi), considering the bivariate Gaussian common component model (BGCCM), which accounts both for the spatial correlation between the two variables and for the individual spatial association. All properties affecting the univariate methodology were verified for ESSbi using simulation studies or algebraic methods, including scenarios to verify the impact of the BGCCM common range parameter on the estimated ESSbi values. ESSbi was applied to real organic matter (OM) and sum of bases (SB) data from an agricultural area. The study found that 60% of the sample observations of the OM–SB pair contained spatially redundant information. The reduced sample configuration proved efficient by preserving spatial variability when comparing the original and reduced OM maps, using SB as a covariate. The Tau concordance index confirmed moderate accuracy between the maps.
有效样本量(ESS)由相同数量的地理参考变量的抽样单元组成,这将产生相同的抽样误差,因为它考虑了每个地理参考抽样单元包含的关于自身以及与其相邻抽样单元的关系的信息。该方法可为今后空间变异性实验的地理参考采样规划提供有用的信息。本文的目的是为ESS (ESSbi)开发一种二元方法,考虑二元高斯共同成分模型(BGCCM),该模型既考虑了两个变量之间的空间相关性,也考虑了个体空间关联。使用模拟研究或代数方法验证了影响单变量方法的所有属性,包括验证BGCCM公共范围参数对估计ESSbi值的影响的场景。将ESSbi应用于某农业区的实有机质(OM)和碱基和(SB)数据。研究发现,60%的OM-SB对样本观测包含空间冗余信息。在比较原始和简化的OM映射时,使用SB作为协变量,简化的样本配置通过保留空间变异性被证明是有效的。Tau一致性指数证实了地图之间的中等准确性。
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引用次数: 0
A Shared Frailty Model for Left-Truncated and Right-Censored Under-Five Child Mortality Data in South Africa 南非五岁以下儿童死亡率数据左截右删的共享脆弱性模型
Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-10-06 DOI: 10.3390/stats6040063
Tshilidzi Mulaudzi, Yehenew Kifle, Roel Braekers
Many African nations continue to grapple with persistently high under-five child mortality rates, particularly those situated in the Sub-Saharan region, including South Africa. A multitude of socio-economic factors are identified as key contributors to the elevated under-five child mortality in numerous African nations. This research endeavors to investigate various factors believed to be associated with child mortality by employing advanced statistical models. This study utilizes child-level survival data from South Africa, characterized by left truncation and right censoring, to fit a Cox proportional hazards model under the assumption of working independence. Additionally, a shared frailty model is applied, clustering children based on their mothers. Comparative analysis is performed between the results obtained from the shared frailty model and the Cox proportional hazards model under the assumption of working independence. Within the scope of this analysis, several factors stand out as significant contributors to under-five child mortality in the study area, including gender, birth province, birth year, birth order, and twin status. Notably, the shared frailty model demonstrates superior performance in modeling the dataset, as evidenced by a lower likelihood cross-validation score compared to the Cox proportional hazards model assuming independence. This improvement can be attributed to the shared frailty model’s ability to account for heterogeneity among mothers and the inherent association between siblings born to the same mother, ultimately enhancing the quality of the study’s conclusions.
许多非洲国家继续努力解决五岁以下儿童死亡率居高不下的问题,特别是在撒哈拉以南地区,包括南非。许多社会经济因素被认为是造成许多非洲国家五岁以下儿童死亡率升高的主要因素。本研究试图通过采用先进的统计模型来调查与儿童死亡率相关的各种因素。本研究利用南非儿童水平的生存数据,采用左截断和右删减的特征,在工作独立性假设下拟合Cox比例风险模型。此外,还应用了共享脆弱性模型,根据母亲对儿童进行聚类。在工作独立性假设下,将共享脆弱性模型与Cox比例风险模型的结果进行对比分析。在本分析的范围内,有几个因素是研究地区五岁以下儿童死亡率的重要因素,包括性别、出生省份、出生年份、出生顺序和双胞胎身份。值得注意的是,与假设独立的Cox比例风险模型相比,共享脆弱性模型在数据集建模方面表现出了卓越的性能,其似然交叉验证得分较低。这种改善可归因于共同脆弱性模型能够解释母亲之间的异质性以及同一母亲所生的兄弟姐妹之间的内在联系,最终提高了研究结论的质量。
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引用次数: 0
Ensemble Algorithms to Improve COVID-19 Growth Curve Estimates 改进COVID-19增长曲线估计的集成算法
Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2023-09-29 DOI: 10.3390/stats6040062
Raydonal Ospina, Jaciele Oliveira, Cristiano Ferraz, André Leite, João Gondim
In January 2020, the world was taken by surprise as a novel disease, COVID-19, emerged, attributed to the new SARS-CoV-2 virus. Initial cases were reported in China, and the virus rapidly disseminated globally, leading the World Health Organization (WHO) to declare it a pandemic on 11 March 2020. Given the novelty of this pathogen, limited information was available regarding its infection rate and symptoms. Consequently, the necessity of employing mathematical models to enable researchers to describe the progression of the epidemic and make accurate forecasts became evident. This study focuses on the analysis of several dynamic growth models, including the logistics, Gompertz, and Richards growth models, which are commonly employed to depict the spread of infectious diseases. These models are integrated to harness their predictive capabilities, utilizing an ensemble modeling approach. The resulting ensemble algorithm was trained using COVID-19 data from the Brazilian state of Paraíba. The proposed ensemble model approach effectively reduced forecasting errors, showcasing itself as a promising methodology for estimating COVID-19 growth curves, improving data forecasting accuracy, and providing rapid responses in the early stages of the pandemic.
2020年1月,一种由新型SARS-CoV-2病毒引起的新型疾病COVID-19的出现震惊了世界。中国报告了首批病例,病毒迅速在全球传播,世界卫生组织(世卫组织)于2020年3月11日宣布其为大流行。鉴于这种病原体的新颖性,关于其感染率和症状的信息有限。因此,利用数学模型使研究人员能够描述流行病的进展并作出准确预测的必要性变得显而易见。本研究重点分析了几种动态增长模型,包括通常用于描述传染病传播的物流、Gompertz和Richards增长模型。利用集成建模方法,将这些模型集成起来,以利用它们的预测能力。所得到的集成算法使用来自巴西Paraíba州的COVID-19数据进行训练。本文提出的集成模型方法有效地减少了预测误差,是估计COVID-19增长曲线、提高数据预测精度和在大流行早期提供快速响应的一种有前途的方法。
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引用次数: 0
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