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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 Q4 STATISTICS & PROBABILITY Pub Date : 2021-02-01 DOI: 10.1214/20-bjps490
H. Saulo, Jeremias Leão, V. Leiva, R. Vila, V. Tomazella
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.
Birnbaum-Saunders分布已被广泛用于建模可靠性和疲劳数据。在本文中,我们提出了一种基于新的二变量Birnbaum–Saunders分布的广义线性模型类型的回归。这是根据其手段参数化的,并允许以原始规模描述数据。我们估计模型参数,并用最大似然法进行推理。为了激励我们的调查,对真实世界的可靠性数据进行了案例研究,说明了所提出的结果的潜在应用。我们获得了一个预测模型,它可以作为不同从业者、可靠性工程师、应用统计学家和数据科学家工具包的有用补充。
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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 Q4 STATISTICS & PROBABILITY Pub Date : 2021-01-01 DOI: 10.1214/20-bjps493
Debjit Sengupta, Surupa Roy, Tathagata Banerjee
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.
对于无界计数数据的建模,泊松分布是一个自然的选择。然而,在科学研究的各个领域中产生的计数数据往往被低估。在这种情况下,基于泊松模型进行的推理将导致参数估计有偏差和次优测试。一个改进的泊松模型被开发以适应可能的低估。为了保证模型的可识别性,采用了双采样的数据采集方案。本文的重点是发展在计数不足的情况下泊松均值的渐近最优检验。进行模拟研究,比较测试在水平和功率方面的性能,并研究忽略漏计数对每个测试的影响。这些发现得到了现实生活数据的验证。
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引用次数: 0
Partitioning some multivariate distributions 多变量分布的划分
IF 1 4区 数学 Q4 STATISTICS & PROBABILITY Pub Date : 2021-01-01 DOI: 10.1214/21-bjps501
J. Kadane
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.
有限集合的划分是该集合的不相交和穷举子集的集合。本文研究了对多元分布进行分划所引起的分布,特别是在每个分划子集内求分划结果的分布,以及分划子集之间的分布。如果多元分布具有独立的单变量分量,则分区会导致每个分区子集内的独立单变量分量。因此,我们的注意力被吸引到没有独立单变量成分的分布上。多元正态分布通常是人们想到的第一个分布。当一个分区仅由两个子集组成时,正态分布可以划分为一个子集以另一个子集为条件,另一个子集为边缘分布。每一个都可以递归划分。然而,结果是正态密度的乘积,它显然取决于划分的顺序,尽管它实际上不能如此依赖,因为每个这样的乘积都重新表达了原始的正态多元分布。在分区中,有两种极端的情况。第一个是最粗糙的分区,包括整个空间。那么这个分划上的分布就是原来的多元分布。另一种极端情况是最好的分区,它的每个子集只有一个组件。那么这个子集上的分布取随机变量的值,其概率为1。因此,本文讨论的分区是介于两者之间的分区,既不是最粗糙的也不是最精细的。
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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 Q4 STATISTICS & PROBABILITY Pub Date : 2021-01-01 DOI: 10.1214/21-bjps498
Julio Hokama, P. Morettin, H. Bolfarine, M. Galea
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.
在本文中,我们考虑了一个具有测量误差的数据分析模型。这项工作的主要目标是开发统计推断工具,如参数估计和假设检验与重复观测的线性函数关系。为此,我们在存在附带参数的情况下使用极大似然方法和无偏估计方程方法。两种方法都可以得到模型参数估计量的渐近协方差矩阵的显式表达式。进行了模拟研究,以评估估计器和Wald统计量的经验行为。用一个实际数据集说明了该方法。
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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 Q4 STATISTICS & PROBABILITY Pub Date : 2021-01-01 DOI: 10.1214/21-bjps499
Do Tran
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.
我们计算了具有绝对连续和旋转对称概率分布的球上fr切特函数的高阶导数。结果包括:(i)一个检验对称分布的模态是否为局部fr平均模态的实际条件;(ii)具有实际假设和显式极限分布的球的中心极限定理;(iii)对于具有绝对连续和旋转对称分布的球体是否可以发生涂抹效应的问题的回答:通过本文提出的方法,它至少可以在4维上发生。
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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 Q4 STATISTICS & PROBABILITY Pub Date : 2021-01-01 DOI: 10.1214/20-bjps485
Teena Goyal, S. Maurya, S. Nadarajah
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.
本文对几何生成的分布族进行了回顾。在此分布族的基础上,提出了几种分布。该族可以通过将零截断几何分布与任何其他模型或分布族的复合概念来提出。在这里,我们提供了一个完整的调查,并列出了贡献的相关研究工作,他们的子模型,危险率,并利用了真实的数据集。我们还讨论了10个幂级数分布,60个基于几何分布族的分布。这些数字显示了几何分布族的重要性。
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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 Q4 STATISTICS & PROBABILITY Pub Date : 2020-12-16 DOI: 10.1214/21-bjps508
R. Mamin, L. Mytnik
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. We 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.
在这项工作中,我们证明了对于任何维度$dgeq1$和(0,1)$超布朗运动中的任何$gamma,对应于log拉普拉斯方程bearth{equipment*}beart{split}frac{partial v(t,x{R}_+timesmathbb{R}^d,v(0,x)&=f(x)end{split}end{。我们的证明是基于LL方程解的性质。我们还证明了当初始数据$v(0,cdot)$是一个有限的非零测度时,LL方程具有唯一的连续解。此外,该解决方案持续依赖于初始数据。
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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 Q4 STATISTICS & PROBABILITY Pub Date : 2020-10-01 DOI: 10.1214/19-BJPS459
Y. Hamura, T. Kubokawa
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.
本文考虑了在加权标准平方误差损失下,可能存在不平衡样本量的独立泊松分布参数的同时估计问题。提出了一类利用样本大小的不平衡性质的非均匀贝叶斯收缩估计。为了提供一个理论证明,我们首先推导了该类估计量是适当贝叶斯因而可容许的充分必要条件,然后得到了与可容许条件相容的极大值的充分条件。通过仿真比较了非均匀收缩估计器和均匀收缩估计器。几种估计方法适用于与标准化死亡率有关的数据。
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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 Q4 STATISTICS & PROBABILITY Pub Date : 2020-10-01 DOI: 10.1214/19-BJPS461
J. Villaseñor, E. González-Estrada
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.
摘要提出了一种基于变换后的观测值和一种新的尺度参数估计量的指数分布拟合检验方法。得到了检验统计量的渐近零分布,并讨论了检验的一致性。蒙特卡罗仿真结果表明,在考虑的备选方案族和样本量下,所提出的测试具有竞争性。
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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 Q4 STATISTICS & PROBABILITY Pub Date : 2020-10-01 DOI: 10.1214/19-BJPS454
N. Kolev
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.
根据Hyman和Shashkov(1997)开发的方法,我们定义了沿连接均匀网格两个节点的任意路径的梯度向量和相关线积分的离散版本。建立了二元离散非负整数值随机变量联合生存函数的离散线积分指数表示。我们将其应用于生成Sibuya型老化特性的离散模拟,结合了许多经典和新的二元离散模型。给出了这类二元离散分布的几个特征和闭包性质。
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引用次数: 2
期刊
Brazilian Journal of Probability and Statistics
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