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The Linear Skew-t Distribution and Its Properties 线性偏t分布及其性质

Stats Pub Date : 2023-02-23 DOI: 10.3390/stats6010024

C. Adcock

{"title":"The Linear Skew-t Distribution and Its Properties","authors":"C. Adcock","doi":"10.3390/stats6010024","DOIUrl":"https://doi.org/10.3390/stats6010024","url":null,"abstract":"The aim of this expository paper is to present the properties of the linear skew-t distribution, which is a specific example of a symmetry modulated-distribution. The skewing function remains the distribution function of Student’s t, but its argument is simpler than that used for the standard skew-t. The linear skew-t offers different insights, for example, different moments and tail behavior, and can be simpler to use for empirical work. It is shown that the distribution may be expressed as a hidden truncation model. The paper describes an extended version of the distribution that is analogous to the extended skew-t. For certain parameter values, the distribution is bimodal. The paper presents expressions for the moments of the distribution and shows that numerical integration methods are required. A multivariate version of the distribution is described. The bivariate version of the distribution may also be bimodal. The distribution is not closed under marginalization, and stochastic ordering is not satisfied. The properties of the distribution are illustrated with numerous examples of the density functions, table of moments and critical values. The results in this paper suggest that the linear skew-t may be useful for some applications, but that it should be used with care for methodological work.","PeriodicalId":93142,"journal":{"name":"Stats","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43915525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On Weak Convergence of the Bootstrap Copula Empirical Process with Random Resample Size 随机样本大小下自举Copula经验过程的弱收敛性

Stats Pub Date : 2023-02-22 DOI: 10.3390/stats6010023

S. Bouzebda

引用次数: 0

Assessing Area under the Curve as an Alternative to Latent Growth Curve Modeling for Repeated Measures Zero-Inflated Poisson Data: A Simulation Study 对重复测量零膨胀泊松数据的曲线下面积评估作为潜在增长曲线模型的替代方法:模拟研究

Stats Pub Date : 2023-02-19 DOI: 10.3390/stats6010022

Daniel Rodriguez

{"title":"Assessing Area under the Curve as an Alternative to Latent Growth Curve Modeling for Repeated Measures Zero-Inflated Poisson Data: A Simulation Study","authors":"Daniel Rodriguez","doi":"10.3390/stats6010022","DOIUrl":"https://doi.org/10.3390/stats6010022","url":null,"abstract":"Researchers interested in the assessment of substance use trajectories, and predictors of change, have several data analysis options. These include, among others, generalized estimating equations and latent growth curve modeling. One difficulty in the assessment of substance use, however, is the nature of the variables studied. Although counting instances of use (e.g., the number of cigarettes smoked per day) would seem to be the best option, such data present difficulties in that the distribution of these variables is not likely normal. Count variables often follow a Poisson distribution, and when dealing with substance use in the general population, there is a preponderance of zeros (representing not using). As such, substance use counts may approximate a zero-inflated Poisson distribution. Unfortunately, analyses with zero-inflated Poisson random variables are not easily accommodated in many types of software and may be beyond access to most researchers. As such, an easier method would benefit researchers interested in assessing substance use change. The purpose of this study is to assess the area under the curve as an option when dealing with repeated measures data and contrast it to one popular method of longitudinal data analysis, latent growth curve modeling. Using a Monte Carlo simulation study with varying sample sizes, we found that the area under the curve performed well with different sample sizes and compared favorably to the performance of latent growth curve modeling, particularly when dealing with smaller sample sizes. The area under the curve may be a simpler alternative for researchers, especially when dealing with smaller sample sizes.","PeriodicalId":93142,"journal":{"name":"Stats","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44589134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Quantum-like Data Modeling in Applied Sciences: Review 应用科学中的类量子数据建模:综述

Stats Pub Date : 2023-02-17 DOI: 10.3390/stats6010021

S. Lipovetsky

引用次数: 2

Panel Data Models for School Evaluation: The Case of High Schools’ Results in University Entrance Examinations 学校评价的面板数据模型:以高中高考成绩为例

Stats Pub Date : 2023-02-13 DOI: 10.3390/stats6010019

Manuel Salas‐Velasco

引用次数: 0

A New Soft-Clipping Discrete Beta GARCH Model and Its Application on Measles Infection 一种新的软剪裁离散Beta GARCH模型及其在麻疹感染中的应用

Stats Pub Date : 2023-02-09 DOI: 10.3390/stats6010018

Huaping Chen