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Brazilian Journal of Probability and Statistics最新文献

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The foundations of statistical science: A history of textbook presentations 统计科学的基础：教科书演示的历史
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2021-11-01 DOI: 10.1214/21-bjps518
A. Agresti
{"title":"The foundations of statistical science: A history of textbook presentations","authors":"A. Agresti","doi":"10.1214/21-bjps518","DOIUrl":"https://doi.org/10.1214/21-bjps518","url":null,"abstract":"We discuss how the foundations of statistical science have been presented historically in textbooks, with focus on the first half of the twentieth century after the field had become better defined by advances due to Francis Galton, Karl Pearson, and R. A. Fisher. Our main emphasis is on books that presented the theory underlying the subject, often identified as mathematical statistics, with primary focus on books authored by G. Udny Yule, Maurice Kendall, Samuel Wilks, and Harald Cramér. We also discuss influential books on statistical methods by R. A. Fisher and George Snedecor that showed scientists how to implement the theory. We then survey textbooks published in the quarter century after World War 2, as Statistics gathered more visibility as an academic subject and Departments of Statistics were formed at many universities. We also summarize how Bayesian presentations of Statistics emerged. In each section, we describe how the books were evaluated in reviews shortly after their publications. We conclude by briefly discussing the recent past, the present, and the future of textbooks on the foundations of statistical science and include comments about this by several notable statisticians.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46794374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Some preservation properties of shifted stochastic orders 移位随机序的一些保存性质
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2021-11-01 DOI: 10.1214/21-bjps510
Sameen Naqvi, N. Misra, P. Chan
{"title":"Some preservation properties of shifted stochastic orders","authors":"Sameen Naqvi, N. Misra, P. Chan","doi":"10.1214/21-bjps510","DOIUrl":"https://doi.org/10.1214/21-bjps510","url":null,"abstract":"In this paper, we provide results on preservation of various shifted stochastic orders under the operations of mixtures. These results have been established with respect to up (down) shifted hazard rate order, up (down) shifted reversed hazard rate order and up (down) shifted likelihood ratio order. In addition, a discussion on preservation of shifted stochastic orders under the operations of convolutions is also presented. Some examples have been obtained to illustrate applications of these results.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47719462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Matrix-variate Lindley distributions and its applications 矩阵变量林德利分布及其应用
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2021-11-01 DOI: 10.1214/21-bjps504
Mariem Tounsi, Mouna Zitouni
{"title":"Matrix-variate Lindley distributions and its applications","authors":"Mariem Tounsi, Mouna Zitouni","doi":"10.1214/21-bjps504","DOIUrl":"https://doi.org/10.1214/21-bjps504","url":null,"abstract":"Abstract. Restring on the fact that the definition of multivariate analogs of the real gamma distribution is replaced by the Wishart distribution on symmetric matrices, and based on the notion of mixture models which is a flexible and powerful tool for treating data taken from multiple subpopulations, we set forward a multivariate analog of the real Lindley distributions of the first and second kinds on the modern framework of symmetric cones which can be used to model waiting and survival times matrix data. Within this framework, we first construct a new probability distributions, named the matrix-variate Lindley distributions. Some fundamental properties of these new distributions are established. Their statistical properties including moments, the coefficient of variation, skewness and the kurtosis are discussed. We then create an iterative hybrid Expectation-Maximization Fisher-Scoring (EM-FS) algorithm to estimate the parameters of the new class of probability distributions. Through simulation as well as comparative studies with respect to the Wishart distribution, the effectiveness and reliability of the proposed distributions are proved. Finally, the usefulness and the applicability of the new models are elaborated and illustrated by means of two real data sets from biological sciences and medical image segmentation which is one of the most important and popular tasks in medical image analysis.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48180642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Componentwise equivariant estimation of order restricted location and scale parameters in bivariate models: A unified study 二元模型中阶限位置和尺度参数的成分等变估计:一个统一的研究
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2021-09-30 DOI: 10.1214/23-bjps562
Naresh Garg, N. Misra
{"title":"Componentwise equivariant estimation of order restricted location and scale parameters in bivariate models: A unified study","authors":"Naresh Garg, N. Misra","doi":"10.1214/23-bjps562","DOIUrl":"https://doi.org/10.1214/23-bjps562","url":null,"abstract":"The problem of estimating location (scale) parameters $theta_1$ and $theta_2$ of two distributions when the ordering between them is known apriori (say, $theta_1leq theta_2$) has been extensively studied in the literature. Many of these studies are centered around deriving estimators that dominate the best location (scale) equivariant estimators, for the unrestricted case, by exploiting the prior information that $theta_1 leq theta_2$. Several of these studies consider specific distributions such that the associated random variables are statistically independent. This paper considers a general bivariate model and general loss function and unifies various results proved in the literature. We also consider applications of these results to a bivariate normal and a Cheriyan and Ramabhadran's bivariate gamma model. A simulation study is also considered to compare the risk performances of various estimators under bivariate normal and Cheriyan and Ramabhadran's bivariate gamma models.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44729736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
On variable selection in joint modeling of mean and dispersion 均值与离散度联合建模中的变量选择
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2021-09-16 DOI: 10.1214/21-bjps512
E. R. Pinto, Leandro Pereira
{"title":"On variable selection in joint modeling of mean and dispersion","authors":"E. R. Pinto, Leandro Pereira","doi":"10.1214/21-bjps512","DOIUrl":"https://doi.org/10.1214/21-bjps512","url":null,"abstract":"The joint modeling of mean and dispersion (JMMD) provides an efficient method to obtain useful models for the mean and dispersion, especially in problems of robust design experiments. However, in the literature on JMMD there are few works dedicated to variable selection and this theme is still a challenge. In this article, we propose a procedure for selecting variables in JMMD, based on hypothesis testing and the quality of the model's fit. A criterion for checking the goodness of fit is used, in each iteration of the selection process, as a filter for choosing the terms that will be evaluated by a hypothesis test. Three types of criteria were considered for checking the quality of the model fit in our variable selection procedure. The criteria used were: the extended Akaike information criterion, the corrected Akaike information criterion and a specific criterion for the JMMD, proposed by us, a type of extended adjusted coefficient of determination. Simulation studies were carried out to verify the efficiency of our variable selection procedure. In all situations considered, the proposed procedure proved to be effective and quite satisfactory. The variable selection process was applied to a real example from an industrial experiment.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45597481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A Monte Carlo integration approach to estimating drift and minorization coefficients for Metropolis–Hastings samplers 估计Metropolis–Hastings采样器漂移系数和二次化系数的蒙特卡罗积分方法
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2021-07-22 DOI: 10.1214/20-bjps486
David A. Spade
{"title":"A Monte Carlo integration approach to estimating drift and minorization coefficients for Metropolis–Hastings samplers","authors":"David A. Spade","doi":"10.1214/20-bjps486","DOIUrl":"https://doi.org/10.1214/20-bjps486","url":null,"abstract":"","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42314760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Log-symmetric models with cure fraction with application to leprosy reactions data 具有治愈率的对数对称模型及其在麻风反应数据中的应用
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2021-07-20 DOI: 10.1214/22-bjps540
J. B. Rocha, F. Medeiros, Dione M. Valencca
{"title":"Log-symmetric models with cure fraction with application to leprosy reactions data","authors":"J. B. Rocha, F. Medeiros, Dione M. Valencca","doi":"10.1214/22-bjps540","DOIUrl":"https://doi.org/10.1214/22-bjps540","url":null,"abstract":"In this paper, we propose a log-symmetric survival model with cure fraction, considering that the distributions of lifetimes for susceptible individuals belong to the log-symmetric class of distributions. This class has continuous, strictly positive, and asymmetric distributions, including the log-normal, log-$t$-Student, Birnbaum-Saunders, log-logistic I, log-logistic II, log-normal-contaminated, log-exponential-power, and log-slash distributions. The log-symmetric class is quite flexible and allows for including bimodal distributions and outliers. This includes explanatory variables through the parameter associated with the cure fraction. We evaluate the performance of the proposed model through extensive simulation studies and consider a real data application to evaluate the effect of factors on the immunity to leprosy reactions in patients with Hansen's disease.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44892910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hypotheses tests on the skewness parameter in a multivariate generalized hyperbolic distribution 多元广义双曲分布中偏度参数的假设检验
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2021-07-01 DOI: 10.1214/21-BJPS502
M. Galea, F. Vilca, C. Zeller
{"title":"Hypotheses tests on the skewness parameter in a multivariate generalized hyperbolic distribution","authors":"M. Galea, F. Vilca, C. Zeller","doi":"10.1214/21-BJPS502","DOIUrl":"https://doi.org/10.1214/21-BJPS502","url":null,"abstract":"The class of generalized hyperbolic (GH) distributions is generated by a mean-variance mixture of a multivariate Gaussian with a generalized inverse Gaussian (GIG) distribution. This rich family of GH distributions includes some well-known heavy-tailed and symmetric multivariate distributions, including the Normal Inverse Gaussian and some members of the family of scale-mixture of skew-normal distributions. The class of GH distributions has received considerable attention in finance and signal processing applications. In this paper, we propose the likelihood ratio (LR) test to test hypotheses about the skewness parameter of a GH distribution. Due to the complexity of the likelihood function, the EM algorithm is used to find the maximum likelihood estimates both in the complete model and the reduced model. For comparative purposes and due to its simplicity, we also consider the Gradient (G) test. A simulation study shows that the LR and G tests are usually able to achieve the desired significance levels and the testing power increases as the asymmetry increases. The methodology developed in the paper is applied to two real datasets.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48933354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inferring association from reliability functions: An approach based on copulas 从可靠性函数推断关联:一种基于copula的方法
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2021-07-01 DOI: 10.1214/20-BJPS491
B. Vineshkumar, N. Nair
{"title":"Inferring association from reliability functions: An approach based on copulas","authors":"B. Vineshkumar, N. Nair","doi":"10.1214/20-BJPS491","DOIUrl":"https://doi.org/10.1214/20-BJPS491","url":null,"abstract":"Nair, Sankaran and John (Metron 76 (2018) 133–153) have defined and studied the properties of reliability functions in terms of copulas. In the present paper, we investigate the utility of such functions in inferring the time-dependent association of bivariate distributions. We consider the Clayton measure of association for the study. A general expression for this measure in terms of the generator of Archimedean copulas is given, and a method of finding nature of association using the generators is provided. We derive the relationship of the association measure with the ageing property of the distribution, associated with the generator. We analyze how the hazard rate of survival copulas can be utilized in studying the association between two random variables. Applications of the results in real life situations are discussed.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48792400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dirac distributions related to sums of independent nonidentically uniform random variables 与独立非同均匀随机变量和有关的狄拉克分布
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2021-07-01 DOI: 10.1214/20-BJPS484
Youssef Lazar, Bander N. Almutairi
{"title":"Dirac distributions related to sums of independent nonidentically uniform random variables","authors":"Youssef Lazar, Bander N. Almutairi","doi":"10.1214/20-BJPS484","DOIUrl":"https://doi.org/10.1214/20-BJPS484","url":null,"abstract":"The aim of this note is to give an elegant proof of a result due to E. G. Olds which concerns the density distribution of the sum of independent uniform random variables non-identically distributed. The proof uses both analytical and combinatorial properties of Dirac distributions and their convolutions. The method is new and can apply to other situations.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47566135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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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