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The New Exponentiated Half Logistic-Harris-G Family of Distributions with Actuarial Measures and Applications 新的具有精算测度的指数半Logistic-Harris-G分布族及其应用
Stats Pub Date : 2023-07-31 DOI: 10.3390/stats6030050
Gayan Warahena-Liyanage, B. Oluyede, Thatayaone Moakofi, Whatmore Sengweni
{"title":"The New Exponentiated Half Logistic-Harris-G Family of Distributions with Actuarial Measures and Applications","authors":"Gayan Warahena-Liyanage, B. Oluyede, Thatayaone Moakofi, Whatmore Sengweni","doi":"10.3390/stats6030050","DOIUrl":"https://doi.org/10.3390/stats6030050","url":null,"abstract":"In this study, we introduce a new generalized family of distributions called the Exponentiated Half Logistic-Harris-G (EHL-Harris-G) distribution, which extends the Harris-G distribution. The motivation for introducing this generalized family of distributions lies in its ability to overcome the limitations of previous families, enhance flexibility, improve tail behavior, provide better statistical properties and find applications in several fields. Several statistical properties, including hazard rate function, quantile function, moments, moments of residual life, distribution of the order statistics and Rényi entropy are discussed. Risk measures, such as value at risk, tail value at risk, tail variance and tail variance premium, are also derived and studied. To estimate the parameters of the EHL-Harris-G family of distributions, the following six different estimation approaches are used: maximum likelihood (MLE), least-squares (LS), weighted least-squares (WLS), maximum product spacing (MPS), Cramér–von Mises (CVM), and Anderson–Darling (AD). The Monte Carlo simulation results for EHL-Harris-Weibull (EHL-Harris-W) show that the MLE method allows us to obtain better estimates, followed by WLS and then AD. Finally, we show that the EHL-Harris-W distribution is superior to some other equi-parameter non-nested models in the literature, by fitting it to two real-life data sets from different disciplines.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41721887","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
Khinchin’s Fourth Axiom of Entropy Revisited 重新审视钦钦的熵的第四公理
Stats Pub Date : 2023-07-27 DOI: 10.3390/stats6030049
Zhiyi Zhang, Hongwei Huang, Hao Xu
{"title":"Khinchin’s Fourth Axiom of Entropy Revisited","authors":"Zhiyi Zhang, Hongwei Huang, Hao Xu","doi":"10.3390/stats6030049","DOIUrl":"https://doi.org/10.3390/stats6030049","url":null,"abstract":"The Boltzmann–Gibbs–Shannon (BGS) entropy is the only entropy form satisfying four conditions known as Khinchin’s axioms. The uniqueness theorem of the BGS entropy, plus the fact that Shannon’s mutual information completely characterizes independence between the two underlying random elements, puts the BGS entropy in a special place in many fields of study. In this article, the fourth axiom is replaced by a slightly weakened condition: an entropy whose associated mutual information is zero if and only if the two underlying random elements are independent. Under the weaker fourth axiom, other forms of entropy are sought by way of escort transformations. Two main results are reported in this article. First, there are many entropies other than the BGS entropy satisfying the weaker condition, yet retaining all the desirable utilities of the BGS entropy. Second, by way of escort transformations, the newly identified entropies are the only ones satisfying the weaker axioms.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42382743","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
Exploring Heterogeneity with Category and Cluster Analyses for Mixed Data 混合数据的分类聚类分析探索异质性
Stats Pub Date : 2023-07-05 DOI: 10.3390/stats6030048
V. Distefano, Maria Mannone, I. Poli
{"title":"Exploring Heterogeneity with Category and Cluster Analyses for Mixed Data","authors":"V. Distefano, Maria Mannone, I. Poli","doi":"10.3390/stats6030048","DOIUrl":"https://doi.org/10.3390/stats6030048","url":null,"abstract":"Precision medicine aims to overcome the traditional one-model-fits-the-whole-population approach that is unable to detect heterogeneous disease patterns and make accurate personalized predictions. Heterogeneity is particularly relevant for patients with complications of type 2 diabetes, including diabetic kidney disease (DKD). We focus on a DKD longitudinal dataset, aiming to find specific subgroups of patients with characteristics that have a close response to the therapeutic treatment. We develop an approach based on some particular concepts of category theory and cluster analysis to explore individualized modelings and achieving insights onto disease evolution. This paper exploits the visualization tools provided by category theory, and bridges category-based abstract works and real datasets. We build subgroups deriving clusters of patients at different time points, considering a set of variables characterizing the state of patients. We analyze how specific variables affect the disease progress, and which drug combinations are more effective for each cluster of patients. The retrieved information can foster individualized strategies for DKD treatment.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46930630","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
Some More Results on Characterization of the Exponential and Related Distributions 关于指数分布及相关分布表征的几个结果
Stats Pub Date : 2023-06-29 DOI: 10.3390/stats6030047
L. Klebanov
{"title":"Some More Results on Characterization of the Exponential and Related Distributions","authors":"L. Klebanov","doi":"10.3390/stats6030047","DOIUrl":"https://doi.org/10.3390/stats6030047","url":null,"abstract":"There are given characterizations of the exponential distribution based on the properties of independence of linear forms with random coefficients. Results based on the constancy of regression of one statistic in a linear form are obtained. Related characterizations based on the property of the identical distribution of statistics are also provided.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48494078","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
Guess for Success? Application of a Mixture Model to Test-Wiseness on Multiple-Choice Exams 猜测成功？混合模型在多项选择题测试中的应用
Stats Pub Date : 2023-06-26 DOI: 10.3390/stats6030046
S. Caudill, F. Mixon
{"title":"Guess for Success? Application of a Mixture Model to Test-Wiseness on Multiple-Choice Exams","authors":"S. Caudill, F. Mixon","doi":"10.3390/stats6030046","DOIUrl":"https://doi.org/10.3390/stats6030046","url":null,"abstract":"The use of large lecture halls in business and economic education often dictates the use of multiple-choice exams to measure student learning. This study asserts that student performance on these types of exams can be viewed as the result of the process of elimination of incorrect answers, rather than the selection of the correct answer. More specifically, how students respond on a multiple-choice test can be broken down into the fractions of questions where no wrong answers can be eliminated (i.e., random guessing), one wrong answer can be eliminated, two wrong answers can be eliminated, and all wrong answers can be eliminated. The results from an empirical model, representing a mixture of binomials in which the probability of a correct choice depends on the number of incorrect choices eliminated, we find, using student performance data from a final exam in principles of microeconomics consisting of 100 multiple choice questions, that the responses to all of the questions on the exam can be characterized by some form of guessing, with more than 26 percent of questions being completed using purely random guessing.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46034470","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
The Gamma-Topp-Leone-Type II-Exponentiated Half Logistic-G Family of Distributions with Applications gamma - topp - leone型ii -指数半Logistic-G族分布及其应用
Stats Pub Date : 2023-06-19 DOI: 10.3390/stats6020045
B. Oluyede, Thatayaone Moakofi
{"title":"The Gamma-Topp-Leone-Type II-Exponentiated Half Logistic-G Family of Distributions with Applications","authors":"B. Oluyede, Thatayaone Moakofi","doi":"10.3390/stats6020045","DOIUrl":"https://doi.org/10.3390/stats6020045","url":null,"abstract":"The new Ristić and Balakhrisnan or Gamma-Topp-Leone-Type II-Exponentiated Half Logistic-G (RB-TL-TII-EHL-G) family of distributions is introduced and investigated in this paper. This work derives and studies some of the main statistical characteristics of this new family of distributions. The maximum likelihood estimation technique is used to estimate the model parameters, and a simulation study is used to assess the consistency of the estimators. Applications to three real-life datasets from various fields show the value and adaptability of the new RB-TL-TII-EHL-G family of distributions. From our results, it is evident that the new proposed distribution is flexible enough to characterize datasets from different fields compared to several other existing distributions in the literature.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41648745","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
Modeling Model Misspecification in Structural Equation Models 结构方程模型中的建模模型错误
Stats Pub Date : 2023-06-14 DOI: 10.3390/stats6020044
A. Robitzsch
{"title":"Modeling Model Misspecification in Structural Equation Models","authors":"A. Robitzsch","doi":"10.3390/stats6020044","DOIUrl":"https://doi.org/10.3390/stats6020044","url":null,"abstract":"Structural equation models constrain mean vectors and covariance matrices and are frequently applied in the social sciences. Frequently, the structural equation model is misspecified to some extent. In many cases, researchers nevertheless intend to work with a misspecified target model of interest. In this article, a simultaneous statistical inference for sampling errors and model misspecification errors is discussed. A modified formula for the variance matrix of the parameter estimate is obtained by imposing a stochastic model for model errors and applying M-estimation theory. The presence of model errors is quantified in increased standard errors in parameter estimates. The proposed inference is illustrated with several analytical examples and an empirical application.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49632752","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
Area under the Curve as an Alternative to Latent Growth Curve Modeling When Assessing the Effects of Predictor Variables on Repeated Measures of a Continuous Dependent Variable 当评估预测变量对连续因变量重复测量的影响时，曲线下面积作为潜在增长曲线模型的替代方法
Stats Pub Date : 2023-05-25 DOI: 10.3390/stats6020043
Daniel Rodriguez
{"title":"Area under the Curve as an Alternative to Latent Growth Curve Modeling When Assessing the Effects of Predictor Variables on Repeated Measures of a Continuous Dependent Variable","authors":"Daniel Rodriguez","doi":"10.3390/stats6020043","DOIUrl":"https://doi.org/10.3390/stats6020043","url":null,"abstract":"Researchers conducting longitudinal data analysis in psychology and the behavioral sciences have several statistical methods to choose from, most of which either require specialized software to conduct or advanced knowledge of statistical methods to inform the selection of the correct model options (e.g., correlation structure). One simple alternative to conventional longitudinal data analysis methods is to calculate the area under the curve (AUC) from repeated measures and then use this new variable in one’s model. The present study assessed the relative efficacy of two AUC measures: the AUC with respect to the ground (AUC-g) and the AUC with respect to the increase (AUC-i) in comparison to latent growth curve modeling (LGCM), a popular repeated measures data analysis method. Using data from the ongoing Panel Study of Income Dynamics (PSID), we assessed the effects of four predictor variables on repeated measures of social anxiety, using both the AUC and LGCM. We used the full information maximum likelihood (FIML) method to account for missing data in LGCM and multiple imputation to account for missing data in the calculation of both AUC measures. Extracting parameter estimates from these models, we next conducted Monte Carlo simulations to assess the parameter bias and power (two estimates of performance) of both methods in the same models, with sample sizes ranging from 741 to 50. The results using both AUC measures in the initial models paralleled those of LGCM, particularly with respect to the LGCM baseline. With respect to the simulations, both AUC measures preformed as well or even better than LGCM in all sample sizes assessed. These results suggest that the AUC may be a viable alternative to LGCM, especially for researchers with less access to the specialized software necessary to conduct LGCM.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43201393","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
A New Extended Weibull Distribution with Application to Influenza and Hepatitis Data 一个新的扩展威布尔分布及其在流感和肝炎数据中的应用
Stats Pub Date : 2023-05-19 DOI: 10.3390/stats6020042
G. Cordeiro, Elisângela C. Biazatti, L. H. de Santana
{"title":"A New Extended Weibull Distribution with Application to Influenza and Hepatitis Data","authors":"G. Cordeiro, Elisângela C. Biazatti, L. H. de Santana","doi":"10.3390/stats6020042","DOIUrl":"https://doi.org/10.3390/stats6020042","url":null,"abstract":"The Weibull is a popular distribution that models monotonous failure rate data. In this work, we introduce the four-parameter Weibull extended Weibull distribution that presents greater flexibility, thus modeling data with bathtub-shaped and unimodal failure rate. Some of its mathematical properties such as quantile function, linear representation and moments are provided. The maximum likelihood estimation is adopted to estimate its parameters, and the log-Weibull extended Weibull regression model is presented. In addition, some simulations are carried out to show the consistency of the estimators. We prove the greater flexibility and performance of this distribution and the regression model through applications to influenza and hepatitis data. The new models perform much better than some of their competitors.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44425313","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
Interval-Censored Regression with Non-Proportional Hazards with Applications 非比例风险区间截尾回归及其应用
Stats Pub Date : 2023-05-17 DOI: 10.3390/stats6020041
F. Prataviera, E. M. Hashimoto, E. M. Ortega, T. Savian, G. Cordeiro
{"title":"Interval-Censored Regression with Non-Proportional Hazards with Applications","authors":"F. Prataviera, E. M. Hashimoto, E. M. Ortega, T. Savian, G. Cordeiro","doi":"10.3390/stats6020041","DOIUrl":"https://doi.org/10.3390/stats6020041","url":null,"abstract":"Proportional hazards models and, in some situations, accelerated failure time models, are not suitable for analyzing data when the failure ratio between two individuals is not constant. We present a Weibull accelerated failure time model with covariables on the location and scale parameters. By considering the effects of covariables not only on the location parameter, but also on the scale, a regression should be able to adequately describe the difference between treatments. In addition, the deviance residuals adapted for data with the interval censored and the exact time of failure proved to be satisfactory to verify the fit of the model. This information favors the Weibull regression as an alternative to the proportional hazards models without masking the effect of the explanatory variables.","PeriodicalId":93142,"journal":{"name":"Stats","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42900574","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
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