The Alpha-Beta-Gamma Skew Normal Distribution and Its Application

In this paper, a new class of skew multimodal distributions with more flexible than alpha skew normal distribution and alpha-beta skew normal distribution is proposed, which makes some important distributions become its special cases. The statistical properties of the new distribution are studied in detail, its moment generating function, skewness coefficient, kurtosis coefficient, Fisher information matrix, maximum likelihood estimators are derived. Moreover, a random simulation study is carried out for test the performance of the estimators, the simulation results show that with the increase of sample size, the mean value of maximum likelihood estimators tends to the true value. The new distribution family provides a better fit compared with other known skew distributions through the analysis of a real data set.

Joint modelling of location and scale parameters of the skew-normal distribution

Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcomes. This paper focuses on the maximum likelihood estimation of joint location and scale models of the skew-normal distribution. The proposed procedure can simultaneously estimate parameters in the location model and the scale model. Simulation studies and a real example are used to illustrate the proposed methodologies.

A Method to Simulate the Skew Normal Distribution

A new method is developed to simulate the skew normal distribution. The result is interesting from a practical as well as a theoretical viewpoint. The new method is simple to program and is more efficient than the standard method of simulation by acceptance-rejection method.

Variable Selection for Robust Mixture Regression Model with Skew Scale Mixtures of Normal Distributions

In this paper, we propose a robust mixture regression model based on the skew scale mixtures of normal distributions (RMR-SSMN) which can accommodate asymmetric, heavy-tailed and contaminated data better. For the variable selection problem, the penalized likelihood approach with a new combined penalty function which balances the SCAD and l2 penalty is proposed. The adjusted EM algorithm is presented to get parameter estimates of RMR-SSMN models at a faster convergence rate. As simulations show, our mixture models are more robust than general FMR models and the new combined penalty function outperforms SCAD for variable selection. Finally, the proposed methodology and algorithm are applied to a real data set and achieve reasonable results.

An Epsilon Half Normal Slash Distribution and Its Applications to Nonnegative Measurements

We introduce a new class of the slash distribution using the epsilon half normal distribution. The newly defined model extends the slashed half normal distribution and has more kurtosis than the ordinary half normal distribution. We study the characterization and properties including moments and some measures based on moments of this distribution. A simulation is conducted to investigate asymptotically the bias properties of the estimators for the parameters. We illustrate its use on a real data set by using maximum likelihood estimation.

A parametric bootstrap approach for one-way classification model with skew-normal random effects

In this paper,several properties of one-way classification model with skew-normal random effects are obtained,such as moment generating function,density function and noncentral skew chi-square distribution,etc.Based on the EM algorithm,we discuss the maximum likelihood(ML)estimation of unknown parameters.For testing problem of fixed effect,a parametric bootstrap(PB)approach is developed.Finally,some simulation results on the Type I error rates and powers of the PB approach are obtained,which show that the PB approach provides satisfactory performances on the Type I error rates and powers,even for small samples.For illustration,our main results are applied to a real data problem.

Bayesian Inference of Spatially Correlated Binary Data Using Skew-Normal Latent Variables with Application in Tooth Caries Analysis

The analysis of spatially correlated binary data observed on lattices is an interesting topic that catches the attention of many scholars of different scientific fields like epidemiology, medicine, agriculture, biology, geology and geography. To overcome the encountered difficulties upon fitting the autologistic regression model to analyze such data via Bayesian and/or Markov chain Monte Carlo (MCMC) techniques, the Gaussian latent variable model has been enrolled in the methodology. Assuming a normal distribution for the latent random variable may not be realistic and wrong, normal assumptions might cause bias in parameter estimates and affect the accuracy of results and inferences. Thus, it entails more flexible prior distributions for the latent variable in the spatial models. A review of the recent literature in spatial statistics shows that there is an increasing tendency in presenting models that are involving skew distributions, especially skew-normal ones. In this study, a skew-normal latent variable modeling was developed in Bayesian analysis of the spatially correlated binary data that were acquired on uncorrelated lattices. The proposed methodology was applied in inspecting spatial dependency and related factors of tooth caries occurrences in a sample of students of Yasuj University of Medical Sciences, Yasuj, Iran. The results indicated that the skew-normal latent variable model had validity and it made a decent criterion that fitted caries data.

偏正态条件下多元线性回归模型的统计推断及其应用

本文考虑带偏正态随机项多元线性回归模型的统计推断问题.基于最大似然方法,本文所做的工作如下:1)证明了参数最大似然估计在n≥p+1条件下以概率1存在唯一;2)在唯一性条件下给出参数估计的一致性结论;3)在一致性的条件下研究了参数的渐近性质,给出参数的渐近分布.最后通过数值模拟说明了所提理论和方法的有效性.实例表明模型参数估计的渐近分布具有实际意义.

带有偏正态误差的众数回归模型最大似然估计的EM算法

经典的多元线性回归模型要求残差满足高斯-马尔柯夫假设(G-M),在实际生活中由于数据的随机性往往很难满足这个条件.利用Sahu等在2003年提出的偏正态分布来拓展经典的回归模型,给出了偏正态分布众数的近似表达式,建立了偏正态分布下均值和众数多元线性回归模型.在求解模型的参数估计时使用偏正态分布的分层表示构造EM算法.在M步统一给出两点步长梯度下降算法,同时也对均值模型给出显示迭代表达式.最后通过模拟分析以及实例来讨论两种回归模型的可行性.

Stochastic ordering of medians in exchangeable trivariate normal vectors

In this paper, we establish the stochastic ordering of median from an exchangeable trivaxiate normal vector based on the strength of the correlation coefficient. Specifically, by considering two exchangeable trivariate normal vectors with different correlation coefficients, we show that the absolute value of the median in the vector with smaller correlation coefficient is stochastically smaller than the absolute value of the median in the vector with larger correlation coefficient. We prove this result by utilizing skew-normal distributions.

基于Pena距离的偏Laplace正态数据下位置回归模型的统计诊断

目前医学、社会学、生物等领域都存在尖峰、厚尾且偏斜的数据,针对这类数据,采用偏Laplace正态数据去拟合,得到的结果会更加精确。同时,在统计学中,异常点或强影响点对统计诊断的结果会产生很大的影响,因此对异常点或强影响点的诊断就显得尤为重要。常用的似然距离、Cook距离等研究删除一个(组)点对回归分析与预测值的影响,而Pena距离研究删除样本中各点对某一特定点回归值以及预测值的影响。基于此,在Pena距离下对偏Laplace正态数据下位置回归模型的影响分析进行了研究,利用EM算法对偏Laplace正态分布下的位置回归模型做了统计诊断。得到偏Laplace正态数据下位置回归模型下Pena距离的表达式以及高杠杆异常点的判别方法,并把Pena距离、Cook距离、似然距离进行比较,得到在某些情况下利用Pena距离检测异常点比Cook距离与似然距离更优。模拟与实例研究说明提出的模型与方法具有合理性。

动态二元偏正态分布的尾相依函数

基于二元正态分布在Hüsler-Reiss条件下有关尾相依函数的研究,再结合二元偏正态相关性质的研究及其尾相依系数的推导,给出了动态二元偏正态分布的在偏度参数大于零和小于零情况下的尾相依函数.

Mathematical Insight into Moderate Inversion Gate Delay Variability for Ultradeep Submicron Digital Circuit Design

Voltage scaling has been extensively used in industry for decades to reduce power consumption.In recent years,exploring digital circuit operation in moderate inversion has created an interest among researchers due to its immense capability to provide a perfect tradeoff between high performance and low energy operation.But circuits operating in moderate inversion are susceptible to process variations and variability.To compute variability,statistical parameters such as the probability density function(PDF)and cumulative distribution function(CDF)are required.This paper presents an analytical model framework for delay calculations utilizing log skew normal distribution for ultradeep submicron technology nodes up to 22 nm.The CDF of the proposed model is utilized to calculate minimum and maximum delays with 3σ-accuracy providing better accuracy than the conventional methods.The obtained results are also compared with Monte Carlo simulations with errors lying within the acceptable range of 2%-4%.

偏正态数据下半参数混合效应模型的贝叶斯估计

针对纵向数据服从非正态分布情况下混合效应模型的估计问题,提出偏正态分布半参数混合效应模型的贝叶斯估计方法;假定个体测量误差服从偏正态分布,纵向指标与时间的关系采用B样条方法建模,在共轭先验下考虑该模型的贝叶斯分析,基于MH算法与Gibbs抽样的混合算法获取未知参数、随机效应和非参数函数的贝叶斯估计;数值模拟中,数据非正态分布条件下将偏正态方法得到的估计与传统半参数混合效应模型估计方法进行对比,发现偏正态半参数混合效应模型在有限样本情况下表现更好,说明偏正态半参数混合效应模型与传统模型相比,可以更好地拟合偏态数据,获得更加精准的参数估计;最后将该方法应用于ADNI数据中,研究了神经评分与基线临床指标间的关系,得出了合理的结论,证明了方法的合理性。

北京市三个功能区空气微生物中值直径及粒径分布特征

空气中微生物对人类健康的危害除了与微生物的种类和浓度有关外,还与微生物粒子的大小密切相关,并且不同粒径的空气微生物对人们健康影响的作用机理不同。通过定点试验调查,运用国产安德森生物粒子取样器着重研究北京市3个功能区(文教区-中国科学院生态环境研究中心所在区域、交通干线-西直门和公园绿地-北京植物园)空气微生物的中值直径和粒径分布。结果表明,不同功能区空气微生物的粒径分布相同,空气细菌,真菌与放线菌的粒径分布各不相同。空气细菌粒径呈偏态分布,空气真菌呈对数正态分布,空气放线菌的分布特征与空气真菌相反,主要分布在>8.2μm和<2.0μm级中。不同属真菌的粒径分布也不相同,枝孢属、青霉属和曲霉属呈对数正态分布,链格孢属和无孢菌为偏态分布。空气细菌的中值直径明显大于空气真菌和放线菌。交通干线和公园绿地空气细菌和真菌粒子中值直径明显大于文教区,放线菌粒子中值直径交通干线明显高于文教区和公园绿地。空气微生物中值直径在一年各月中没有明显的变化规律。

均匀泥沙相对暴露度的试验研究

以杨奉广建立的相对暴露度概念为基础，通过自行设计的试验装置，测量了均匀玻璃球的暴露角和河卵石的绝对暴露度，分析计算了其相对暴露度及其分布规律。结果表明，玻璃球相对暴露度取值范围介于0～0．5之间，暴露角呈正态分布，相对暴露度呈偏正态分布；在此基础上，利用实测资料对暴露角正态分布公式中的系数进行了率定，通过暴露角和相对暴露度概率密度函数转换，给出了相对暴露度概率密度函数；河卵石相对暴露度取值范围也介于0～0．5之间，相对暴露度呈偏正态分布，与本文公式的分布曲线不完全重合，说明河卵石复杂外形、粒径和形心的不同对其相对暴露度概率密度分布曲线的影响较大。

用LMS法建立西安市0～18岁人群体重百分位数曲线

目的 年龄别百分位数是许多临床参考值的基本参数,本文研究一种适合于任意分布,能更精确描述这些基本参数随年龄变化的曲线平滑方法。方法 采用LMS法建立西安市0～18岁人群青少年体重百分位数曲线。结果 给出了各组的年龄别L,M,S曲线和百分位数曲线。结论 该法用于西安市0～18岁人群体重百分位数曲线的拟合结果非常满意。

内蒙古典型草原动态监测的取样问题

本文用数理统计方法 ,对内蒙古典型草原地带的羊草 +大针茅草原群落 2 0年 ( 1 981-2 0 0 0 )的采样数据进行分析、检验 ,选择出群落中的重要种 ,验证了草原的物种生物量服从正态分布 ,并证明了在采样中取 1 0个样方的生物量统计 ,即可替代 2

基于广义偏斜正态分布的分配曲线数学模型

为提高分配曲线数学模型的适应性,并进一步明确分配曲线数学模型中的参数意义,以含偏斜系数的3参数广义正态分布函数为基础,新增一个峰度系数,构建了一个直接由分选密度、可能偏差、偏斜系数和峰度系数作参数的4参数分配曲线数学模型。经过对重介旋流器、跳汰机、螺旋分选机等16组分配曲线数据的检验,模型均有良好的拟合精度。偏斜系数和峰度系数对分配曲线的对称性及其两端的形态具有良好的指示作用:偏度系数为正值,曲线发生左偏,低密度物损失加大;偏度系数为负值,曲线发生右偏,高密度物污染加大;峰度系数主要影响分配曲线两端的形态,峰度系数大,两端的分选精度高。同时提出了一个5参数的数学模型,可进一步提高拟合精度。

偏正态全波激光雷达数据的可变分量波形分解

针对传统方法难以实现全波激光雷达数据中非对称波形分解的问题,本文提出一种结合可变分量偏正态模型和可逆跳马尔科夫链蒙特卡洛(RJMCMC)算法的波形分解方法。首先,利用能量函数刻画服从偏正态分布的理想波形与实际波形间的差异程度,并用Gibbs分布定义其似然函数;然后,定义理想波形参数模型的先验分布;在贝叶斯定理框架下,建立具有分量可变性的波形分解模型;设计RJMCMC的移动操作,确定偏正态分布中的分量数以及求解模型参数。利用提出算法,对不同波形特征(偏态、正态)的ICESat-GLAS全波激光雷达数据进行可变分量分解实验。实验结果表明:实验波形结果与实际波形数据相关系数达到0.989以上,所提方法不仅能够同时实现对偏态数据和正态数据的拟合,还能更为准确地确定波形分量数。证明了该方法能实现全波激光雷达数据的精确分解,且分解结果与对应地物高程信息相符。