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Brazilian Journal of Probability and Statistics最新文献

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A bivariate fatigue-life regression model and its application to fracture of metallic tools 二元疲劳寿命回归模型及其在金属工具断裂中的应用
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2021-02-01 DOI: 10.1214/20-bjps490
H. Saulo, Jeremias Leão, V. Leiva, R. Vila, V. Tomazella
{"title":"A bivariate fatigue-life regression model and its application to fracture of metallic tools","authors":"H. Saulo, Jeremias Leão, V. Leiva, R. Vila, V. Tomazella","doi":"10.1214/20-bjps490","DOIUrl":"https://doi.org/10.1214/20-bjps490","url":null,"abstract":"The Birnbaum–Saunders distribution has been widely used to model reliability and fatigue data. In this paper, we propose a regression of generalized linear models type based on a new bivariate Birnbaum–Saunders distribution. This is parameterized in terms of its means and allows data to be described in their original scale. We estimate the model parameters and carry out inference with the maximum likelihood method. A case study with real-world reliability data is conducted for motivating our investigation, illustrating the potential applications of the proposed results. We obtain a predictive model which can be a useful addition to the tool-kit of diverse practitioners, reliability engineers, applied statisticians, and data scientists.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48604845","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
Testing of Poisson mean with under-reported counts 漏报计数的泊松平均值检验
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2021-01-01 DOI: 10.1214/20-bjps493
Debjit Sengupta, Surupa Roy, Tathagata Banerjee
{"title":"Testing of Poisson mean with under-reported counts","authors":"Debjit Sengupta, Surupa Roy, Tathagata Banerjee","doi":"10.1214/20-bjps493","DOIUrl":"https://doi.org/10.1214/20-bjps493","url":null,"abstract":"For modelling unbounded count data, Poisson distribution is a natural choice. However, count data arising in various fields of scientific research are often under-reported. In such situations, inference carried out on the basis of Poisson model will result in biased parameter estimates and suboptimal tests. A modified Poisson model is developed to accommodate the possible undercount. For model-identifiability a double sampling scheme of data collection has been adopted. The focus of this paper is to develop asymptotically optimal tests for the Poisson mean in presence of undercount. Simulation study is conducted to compare the performance of the tests with respect to level and power and also to investigate the impact of ignoring undercount on each of the tests. The findings are validated using real life data.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66081375","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
Partitioning some multivariate distributions 多变量分布的划分
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2021-01-01 DOI: 10.1214/21-bjps501
J. Kadane
{"title":"Partitioning some multivariate distributions","authors":"J. Kadane","doi":"10.1214/21-bjps501","DOIUrl":"https://doi.org/10.1214/21-bjps501","url":null,"abstract":"A partition of a finite set is a collection of disjoint and exhaustive subsets of that set. This paper concerns the distributions occasioned by partitioning a multivariate distribution, in particular to find the resultant distribution within each partition subset, and the distribution between them. If the multivariate distribution has independent univariate components, then partitioning leads to independent univariate components within each partition subset. Consequently, our attention is drawn to distributions without independent univariate components. The multivariate normal distribution is often the first such distribution that one thinks of. When a partition consists of only two subsets, the normal distribution can be partitioned into a conditional of one subset conditioned on the other, and a marginal distribution on the second subset. And each of these can be recursively partitioned. The result, however, is a product of normal densities that apparently depends on the order in which the partitioning is done, although it cannot in fact so depend, as each such product re-expresses the original normal multivariate distribution. Among partitions, there are two extreme cases. The first is the coarsest possible partition, consisting of the whole space. Then trivially the distribution over this partition is the original multivariate distribution, whatever it was. The other extreme case is a finest possible partition, each subset of which has only a single component. Then the distribution on such a subset takes the value of the random variable with probability one. So the partitions at issue in this paper are the partitions in-between, neither the coarsest nor the finest.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66085825","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
Inference in a linear functional relationship with replications 与复制的线性函数关系中的推论
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2021-01-01 DOI: 10.1214/21-bjps498
Julio Hokama, P. Morettin, H. Bolfarine, M. Galea
{"title":"Inference in a linear functional relationship with replications","authors":"Julio Hokama, P. Morettin, H. Bolfarine, M. Galea","doi":"10.1214/21-bjps498","DOIUrl":"https://doi.org/10.1214/21-bjps498","url":null,"abstract":"In this paper, we consider a model for data analysis with measurement errors. The main objective of this work is to develop statistical inference tools, such as parameter estimation and hypothesis tests in a linear functional relationship with replicated observations. For this purpose, we use the maximum likelihood method in the presence of incidental parameters, and the unbiased estimating equations approach. Both approaches lead to explicit expressions for the asymptotic covariance matrices of the estimators of the model parameters. A simulation study is performed to assess the empirical behavior of estimators and of a Wald statistic. The methodology is illustrated with a real data set.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66085761","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
Behavior of the Fréchet mean and Central Limit Theorems on spheres 球面上fr<s:1>均值定理和中心极限定理的性质
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2021-01-01 DOI: 10.1214/21-bjps499
Do Tran
{"title":"Behavior of the Fréchet mean and Central Limit Theorems on spheres","authors":"Do Tran","doi":"10.1214/21-bjps499","DOIUrl":"https://doi.org/10.1214/21-bjps499","url":null,"abstract":"We compute higher derivatives of the Fréchet function on spheres with an absolutely continuous and rotationally symmetric probability distribution. Consequences include (i) a practical condition to test if the mode of the symmetric distribution is a local Fréchet mean; (ii) a Central Limit Theorem on spheres with practical assumptions and an explicit limiting distribution; and (iii) an answer to the question of whether the smeary effect can occur on spheres with absolutely continuous and rotationally symmetric distributions: with the method presented here, it can in dimension at least 4.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66085811","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
Geometric generated family of distributions: A review 几何生成分布族:综述
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2021-01-01 DOI: 10.1214/20-bjps485
Teena Goyal, S. Maurya, S. Nadarajah
{"title":"Geometric generated family of distributions: A review","authors":"Teena Goyal, S. Maurya, S. Nadarajah","doi":"10.1214/20-bjps485","DOIUrl":"https://doi.org/10.1214/20-bjps485","url":null,"abstract":"The present article represents a review of the geometric generated family of distributions. Based on this family of distribution, several distributions are proposed. The family can be proposed by using the compounding concept of zero truncated geometric distribution with any other model or family of distributions. Here, we provide a complete survey on this family of distributions and also listed the contributory related research work, their sub-models, hazard rates, and utilized real datasets. We also address 10 power series distributions, 60 distributions based on the geometric family of distribution. These numbers show the importance of the geometric family of distribution.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66081249","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
Absolute continuity of the super-Brownian motion with infinite mean 具有无限均值的超布朗运动的绝对连续性
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2020-12-16 DOI: 10.1214/21-bjps508
R. Mamin, L. Mytnik
{"title":"Absolute continuity of the super-Brownian motion with infinite mean","authors":"R. Mamin, L. Mytnik","doi":"10.1214/21-bjps508","DOIUrl":"https://doi.org/10.1214/21-bjps508","url":null,"abstract":"In this work we prove that for any dimension $dgeq 1$ and any $gamma in (0,1)$ super-Brownian motion corresponding to the log-Laplace equation begin{equation*} begin{split} frac{partial v(t,x)}{partial t } & = frac{1}{2}bigtriangleup v(t,x) + v^gamma (t,x) ,: (t,x) in mathbb{R}_+times mathbb{R}^d, v(0,x)&= f(x) end{split} end{equation*} is absolutely continuous with respect to the Lebesgue measure at any fixed time $t>0$. Our proof is based on properties of solutions of the LL equation. \u0000We also prove that when initial datum $v(0,cdot)$ is a finite, non-zero measure, then the LL equation has a unique, continuous solution. Moreover this solution continuously depends on initial data.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44355568","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
Proper Bayes minimax estimation of parameters of Poisson distributions in the presence of unbalanced sample sizes 不平衡样本量下泊松分布参数的适当贝叶斯极大极小估计
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2020-10-01 DOI: 10.1214/19-BJPS459
Y. Hamura, T. Kubokawa
{"title":"Proper Bayes minimax estimation of parameters of Poisson distributions in the presence of unbalanced sample sizes","authors":"Y. Hamura, T. Kubokawa","doi":"10.1214/19-BJPS459","DOIUrl":"https://doi.org/10.1214/19-BJPS459","url":null,"abstract":"In this paper, we consider the problem of simultaneously estimating parameters of independent Poisson distributions in the presence of possibly unbalanced sample sizes under weighted standardized squared error loss. A class of heterogeneous Bayesian shrinkage estimators that utilize the unbalanced nature of sample sizes is proposed. To provide a theoretical justification, we first derive a necessary and sufficient condition for an estimator in the class to be proper Bayes and hence admissible and then obtain sufficient conditions for minimaxity that are compatible with the admissibility condition. Heterogeneous and homogeneous shrinkage estimators are compared by simulation. Several estimation methods are applied to data relating to the standardized mortality ratio.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48926993","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
On testing exponentiality based on a new estimator for the scale parameter 基于一种新的标度参数估计器的指数性检验
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2020-10-01 DOI: 10.1214/19-BJPS461
J. Villaseñor, E. González-Estrada
{"title":"On testing exponentiality based on a new estimator for the scale parameter","authors":"J. Villaseñor, E. González-Estrada","doi":"10.1214/19-BJPS461","DOIUrl":"https://doi.org/10.1214/19-BJPS461","url":null,"abstract":"Abstract. A test of fit for the exponential distribution is presented, which is based on transformed observations and a new estimator for the scale parameter. The asymptotic null distribution of the test statistic is obtained and the consistency of the test is discussed. Monte Carlo simulation results on a power comparison study show that the proposed test is competitive under the considered families of alternatives and sample sizes.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41442785","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
Discrete line integral on uniform grids: Probabilistic interpretation and applications 均匀网格上的离散线积分:概率解释和应用
IF 1 4区 数学
Brazilian Journal of Probability and Statistics Pub Date : 2020-10-01 DOI: 10.1214/19-BJPS454
N. Kolev
{"title":"Discrete line integral on uniform grids: Probabilistic interpretation and applications","authors":"N. Kolev","doi":"10.1214/19-BJPS454","DOIUrl":"https://doi.org/10.1214/19-BJPS454","url":null,"abstract":"Following the methodology developed by Hyman and Shashkov (1997), we define a discrete version of gradient vector and associated line integral along arbitrary path connecting two nodes of uniform grid. An exponential representation of joint survival function of bivariate discrete non-negative integer-valued random variables in terms of discrete line integral is established. We apply it to generate a discrete analogue of the Sibuya-type aging property, incorporating many classical and new bivariate discrete models. Several characterizations and closure properties of this class of bivariate discrete distributions are presented.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46643372","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
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