Journal of Statistical Distributions and Applications最新文献

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Mean and variance of ratios of proportions from categories of a multinomial distribution 多项分布类别中比例比率的均值和方差

Q2 Mathematics

Journal of Statistical Distributions and Applications

Pub Date : 2018-01-18 DOI: 10.1186/s40488-018-0083-x

Frantisek Duris, Juraj Gazdarica, Iveta Gazdaricova, Lucia Strieskova, Jaroslav Budis, Jan Turna, Tomas Szemes

Ratio distribution is a probability distribution representing the ratio of two random variables, each usually having a known distribution. Currently, there are results when the random variables in the ratio follow (not necessarily the same) Gaussian, Cauchy, binomial or uniform distributions. In this paper we consider a case, where the random variables in the ratio are joint binomial components of a multinomial distribution. We derived formulae for mean and variance of this ratio distribution using a simple Taylor-series approach and also a more complex approach which uses a slight modification of the original ratio. We showed that the more complex approach yields better results with simulated data. The presented results can be directly applied in the computation of confidence intervals for ratios of multinomial proportions. AMS Subject Classification: 62E20

比率分布是一种概率分布，表示两个随机变量的比率，每个随机变量通常有一个已知的分布。目前，当比率中的随机变量遵循(不一定相同)高斯分布，柯西分布，二项分布或均匀分布时，有结果。本文考虑一种情况，其中比率中的随机变量是多项分布的联合二项式分量。我们使用简单的泰勒级数方法和一种更复杂的方法推导了该比率分布的均值和方差公式，该方法对原始比率进行了轻微的修改。我们表明，更复杂的方法产生更好的结果与模拟数据。所得结果可直接应用于多项式比例比置信区间的计算。AMS学科分类:62E20

引用次数: 14

The power-Cauchy negative-binomial: properties and regression 幂-柯西负二项式:性质与回归

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Journal of Statistical Distributions and Applications

Pub Date : 2018-01-08 DOI: 10.1186/s40488-017-0082-3

Muhammad Zubair, Muhammad H. Tahir, Gauss M. Cordeiro, Ayman Alzaatreh, Edwin M. M. Ortega

We propose and study a new compounded model to extend the half-Cauchy and power-Cauchy distributions, which offers more flexibility in modeling lifetime data. The proposed model is analytically tractable and can be used effectively to analyze censored and uncensored data sets. Its density function can have various shapes such as reversed-J and right-skewed. It can accommodate different hazard shapes such as decreasing, upside-down bathtub and decreasing-increasing-decreasing. Some mathematical properties of the new distribution can be determined from a linear combination for its density function such as ordinary and incomplete moments. The performance of the maximum likelihood method to estimate the model parameters is investigated by a simulation study. Further, we introduce the new log-power-Cauchy negative-binomial regression model for censored data, which includes as sub-models some widely known regression models that can be applied to censored data. Four real life data sets, of which one is censored, have been analyzed and the new models provide adequate fits.

我们提出并研究了一种新的复合模型来扩展半柯西分布和幂柯西分布，为建模生命周期数据提供了更大的灵活性。该模型易于分析处理，可以有效地用于分析删减和未删减的数据集。它的密度函数可以有各种形状，如反j型和右斜型。可适应减小型、倒浴盆型、减小-增大-减小型等不同的危险形态。新分布的一些数学性质可以由其密度函数的线性组合来确定，如普通矩和不完全矩。通过仿真研究了极大似然法估计模型参数的性能。此外，我们引入了新的对数幂-柯西负二项回归模型，该模型包括一些广泛应用于审查数据的回归模型作为子模型。分析了四个真实生活数据集，其中一个被删减，新模型提供了足够的拟合。

引用次数: 3

A nonparametric approach for quantile regression. 分位数回归的一种非参数方法。

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Journal of Statistical Distributions and Applications

Pub Date : 2018-01-01 Epub Date: 2018-07-18 DOI: 10.1186/s40488-018-0084-9

Mei Ling Huang, Christine Nguyen

Quantile regression estimates conditional quantiles and has wide applications in the real world. Estimating high conditional quantiles is an important problem. The regular quantile regression (QR) method often designs a linear or non-linear model, then estimates the coefficients to obtain the estimated conditional quantiles. This approach may be restricted by the linear model setting. To overcome this problem, this paper proposes a direct nonparametric quantile regression method with five-step algorithm. Monte Carlo simulations show good efficiency for the proposed direct QR estimator relative to the regular QR estimator. The paper also investigates two real-world examples of applications by using the proposed method. Studies of the simulations and the examples illustrate that the proposed direct nonparametric quantile regression model fits the data set better than the regular quantile regression method.

分位数回归估计条件分位数，在现实世界中有着广泛的应用。估计高条件分位数是一个重要的问题。正则分位数回归（QR）方法通常设计线性或非线性模型，然后估计系数以获得估计的条件分位数。这种方法可能受到线性模型设置的限制。为了克服这一问题，本文提出了一种五步算法的直接非参数分位数回归方法。蒙特卡罗模拟表明，相对于常规QR估计，所提出的直接QR估计具有良好的效率。本文还使用所提出的方法研究了两个实际应用实例。仿真和实例研究表明，所提出的直接非参数分位数回归模型比常规分位数回归方法更适合数据集。

引用次数: 3

Parameters of stochastic models for electroencephalogram data as biomarkers for child's neurodevelopment after cerebral malaria. 脑电图数据随机模型参数作为脑疟疾后儿童神经发育的生物标志物。

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Journal of Statistical Distributions and Applications

Pub Date : 2018-01-01 Epub Date: 2018-12-29 DOI: 10.1186/s40488-018-0086-7

Maria A Veretennikova, Alla Sikorskii, Michael J Boivin

The objective of this study was to test statistical features from the electroencephalogram (EEG) recordings as predictors of neurodevelopment and cognition of Ugandan children after coma due to cerebral malaria. The increments of the frequency bands of EEG time series were modeled as Student processes; the parameters of these Student processes were estimated and used along with clinical and demographic data in a machine-learning algorithm for the prediction of children's neurodevelopmental and cognitive scores 6 months after cerebral malaria illness. The key innovation of this work is in the identification of stochastic EEG features that can serve as language-independent markers of the impact of cerebral malaria on the developing brain. The results can enhance prognostic determination of which children are in most need of rehabilitative interventions, which is especially important in resource-constrained settings such as sub-Saharan Africa.

本研究的目的是测试脑电图(EEG)记录的统计特征作为乌干达儿童脑疟疾昏迷后神经发育和认知的预测因子。将脑电时间序列的频带增量建模为Student过程;这些学生过程的参数被估计，并与临床和人口统计数据一起用于机器学习算法，以预测脑疟疾后6个月儿童的神经发育和认知评分。这项工作的关键创新在于识别随机脑电图特征，这些特征可以作为脑疟疾对发育中的大脑影响的语言无关标记。研究结果可以加强对哪些儿童最需要康复干预的预后判断，这在撒哈拉以南非洲等资源受限的环境中尤为重要。

引用次数: 6

Families of distributions arising from the quantile of generalized lambda distribution 广义λ分布的分位数所产生的分布族

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Journal of Statistical Distributions and Applications

Pub Date : 2017-11-22 DOI: 10.1186/s40488-017-0081-4

Mahmoud Aldeni, Carl Lee, Felix Famoye

In this paper, the class of T-R {generalized lambda} families of distributions based on the quantile of generalized lambda distribution has been proposed using the T-R{Y} framework. In the development of the T-R{Y} framework, the support of Y and T must be the same. It is typical that the random variable Y has one type of support and T is restricted to the same support. Taking Y to be a generalized lambda random variable leads to three different types of supports, thus, making the choice of the generator T to be much more broad and flexible. This is interesting and unique. By allowing T with different supports makes the T-R{generalized lambda} a desirable method for generating new versatile and broad families of generalized distributions for any given random variable R. Some general properties of these families of distributions are studied. Four members of the T-R{generalized lambda} families of distributions are derived. The shapes of these distributions can be symmetric, skewed to the left, skewed to the right, or bimodal. Two real life data sets are applied to illustrate the flexibility of the distributions.

本文利用T-R{Y}框架，基于广义λ分布的分位数，提出了一类T-R{广义λ}族分布。在开发T- r {Y}框架时，Y和T的支持必须是相同的。典型的情况是，随机变量Y有一种支持，而T被限制为同一种支持。将Y作为广义的lambda随机变量，可以得到三种不同类型的支撑，从而使发电机T的选择更加广泛和灵活。这很有趣，也很独特。通过允许T具有不同的支撑点，使得T- r{广义λ}成为对任意给定的随机变量r生成新的通用的广义分布族的理想方法。导出了T-R{广义λ}族分布的四个成员。这些分布的形状可以是对称的、向左倾斜的、向右倾斜的或双峰的。本文应用了两个实际数据集来说明分布的灵活性。

引用次数: 27

Risk ratios and Scanlan’s HRX 风险比和斯坎兰的HRX

Q2 Mathematics

Journal of Statistical Distributions and Applications

Pub Date : 2017-11-15 DOI: 10.1186/s40488-017-0071-6

H. Thomas, T. Hettmansperger

引用次数: 3

Joint distribution of k-tuple statistics in zero-one sequences of Markov-dependent trials 马尔可夫相关试验0 - 1序列中k元组统计量的联合分布

Q2 Mathematics

Journal of Statistical Distributions and Applications

Pub Date : 2017-11-15 DOI: 10.1186/s40488-017-0080-5

Anastasios N. Arapis, Frosso S. Makri, Zaharias M. Psillakis

We consider a sequence of n, n≥3, zero (0) - one (1) Markov-dependent trials. We focus on k-tuples of 1s; i.e. runs of 1s of length at least equal to a fixed integer number k, 1≤k≤n. The statistics denoting the number of k-tuples of 1s, the number of 1s in them and the distance between the first and the last k-tuple of 1s in the sequence, are defined. The work provides, in a closed form, the exact conditional joint distribution of these statistics given that the number of k-tuples of 1s in the sequence is at least two. The case of independent and identical 0−1 trials is also covered in the study. A numerical example illustrates further the theoretical results.

我们考虑一个序列n, n≥3,0(0)- 1(1)个马尔可夫相关试验。我们关注的是1的k元组;即运行1次，长度至少等于一个固定整数k, 1≤k≤n。定义了表示包含1的k元组的个数、其中包含的1个数以及序列中第一个包含1的k元组与最后一个包含1的k元组之间的距离的统计量。本文以一种封闭的形式给出了这些统计量的精确条件联合分布，假设序列中包含1的k元组的个数至少为两个。独立和相同的0 - 1试验的情况也包括在研究中。数值算例进一步说明了理论结果。

引用次数: 0

A useful extension of the Burr III distribution Burr III分布的一个有用的扩展

Q2 Mathematics

Journal of Statistical Distributions and Applications

Pub Date : 2017-11-01 DOI: 10.1186/s40488-017-0079-y

Gauss M. Cordeiro, Antonio E. Gomes, Cibele Q. da-Silva, Edwin M. M. Ortega

For any continuous baseline G distribution, Zografos and Balakrishnan (Statistical Methodology 6:344–362, 2009) introduced the gamma-generated family of distributions with an extra shape parameter. Based on this family, we define a new four-parameter extension of the Burr III distribution. It can have decreasing, unimodal and decreasing-increasing-decreasing hazard rate function. We provide a comprehensive account of some of its structural properties. We propose a new log-gamma Burr III regression model, which is a feasible alternative for modeling the four existing types of failure rates. Two applications to real data sets and a simulation study illustrate the performance of the new models.

对于任何连续基线G分布，Zografos和Balakrishnan (Statistical Methodology 6:34 - 362, 2009)引入了具有额外形状参数的伽玛生成分布族。在此基础上，我们定义了Burr III分布的一个新的四参数扩展。它可以具有递减、单峰和递减-递增-递减的危险率函数。我们提供了它的一些结构特性的全面说明。我们提出了一个新的log-gamma Burr III回归模型，这是一个可行的替代建模现有的四种类型的故障率。两个实际数据集的应用和仿真研究说明了新模型的性能。

引用次数: 7

Describing the Flexibility of the Generalized Gamma and Related Distributions 描述广义伽玛分布和相关分布的灵活性

Q2 Mathematics

Journal of Statistical Distributions and Applications

Pub Date : 2017-11-01 DOI: 10.1186/s40488-017-0072-5

Matthew Matheson, Alvaro Muñoz, Christopher Cox

The generalized gamma (GG) distribution is a widely used, flexible tool for parametric survival analysis. Many alternatives and extensions to this family have been proposed. This paper characterizes the flexibility of the GG by the quartile ratio relationship, log(Q2/Q1)/log(Q3/Q2), and compares the GG on this basis with two other three-parameter distributions and four parent distributions of four or five parameters. For most parameter combinations of other distributions, a very similar GG, as assessed by the Kullback-Liebler distance, can be found by matching the three quartiles; extreme cases where this fails are examined. Limited additional flexibility is observed, supporting the basic GG family as an ideal platform for parametric survival analysis.

广义γ (GG)分布是一种广泛使用的、灵活的参数生存分析工具。人们提出了这个家庭的许多替代方案和扩展。本文通过对数(Q2/Q1)/对数(Q3/Q2)的四分位数比值关系表征了GG的灵活性，并在此基础上将GG与另外两个三参数分布和四个四或五个参数的父分布进行了比较。对于其他分布的大多数参数组合，可以通过匹配三个四分位数找到非常相似的GG，如通过Kullback-Liebler距离评估;研究了这种方法失败的极端情况。观察到有限的额外灵活性，支持基本GG家族作为参数生存分析的理想平台。

引用次数: 5

Quantile regression for overdispersed count data: a hierarchical method 过度分散计数数据的分位数回归:一种分层方法

Q2 Mathematics

Journal of Statistical Distributions and Applications

Pub Date : 2017-11-01 DOI: 10.1186/s40488-017-0073-4

Peter Congdon

Generalized Poisson regression is commonly applied to overdispersed count data, and focused on modelling the conditional mean of the response. However, conditional mean regression models may be sensitive to response outliers and provide no information on other conditional distribution features of the response. We consider instead a hierarchical approach to quantile regression of overdispersed count data. This approach has the benefits of effective outlier detection and robust estimation in the presence of outliers, and in health applications, that quantile estimates can reflect risk factors. The technique is first illustrated with simulated overdispersed counts subject to contamination, such that estimates from conditional mean regression are adversely affected. A real application involves ambulatory care sensitive emergency admissions across 7518 English patient general practitioner (GP) practices. Predictors are GP practice deprivation, patient satisfaction with care and opening hours, and region. Impacts of deprivation are particularly important in policy terms as indicating effectiveness of efforts to reduce inequalities in care sensitive admissions. Hierarchical quantile count regression is used to develop profiles of central and extreme quantiles according to specified predictor combinations.

广义泊松回归通常应用于过度分散的计数数据，并侧重于模拟响应的条件均值。然而，条件均值回归模型可能对响应异常值敏感，无法提供响应的其他条件分布特征的信息。我们考虑采用分层方法对过度分散的计数数据进行分位数回归。这种方法具有在存在异常值时有效检测异常值和稳健估计的优点，并且在卫生应用中，分位数估计可以反映风险因素。该技术首先用受污染影响的模拟过分散计数来说明，这样，条件平均回归的估计就会受到不利影响。一个真实的应用涉及门诊护理敏感急诊招生跨越7518名英国病人全科医生(GP)的做法。预测因子是全科医生执业剥夺、患者对护理和开放时间的满意度以及地区。剥夺的影响在政策方面特别重要，因为它表明减少护理敏感入院不平等现象的努力是否有效。分层分位数计数回归用于根据指定的预测器组合开发中心和极端分位数的概况。

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引用次数: 9

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