Friday and Patil's Bivariate Exponential Distribution with Application to Drought Data

Motivated by hydrological applications, we derive the exact distributions of R = X + Y, P = XY and W = X/(X+Y) and the corresponding moment properties when X and Y follow Friday and Patil's bivariate exponential distribution. An application of the results is provided to drought data from Nebraska.     

Product Moments of Downton’s Bivariate Exponential Distribution

Downton’s bivariate exponential distribution has been a popular model for hydrological sciences. However, it seems that no explicit expressions for its product moments are available. In this short note, we provide a direct derivation of a general expression for the product moments and also derive several particular forms. An application of the results is illustrated using drought data from the State of Nebraska.     

ISO13528与NATA能力验证尧敦图的统计模型比较

对ISO13528和澳大利亚国家检测机构协会(NATA)所用的能力验证尧敦图的统计模型进行了讨论,分别利用霍特林T²检验和二维正态分布推导出尧敦椭圆方程的公式,使用Excel软件绘制出尧敦椭圆,参与能力验证的各个实验室的分析数据也在同一个图中显示出来。利用坐标变换,还得到了其他不同坐标下的尧敦图。在一个尧敦图中同时绘制出置信水平分别为95%和99%的尧敦椭圆,直观显示出合格数据、存疑数据和不合格数据。ISO 13528中,Z_A,B是系统误差和随机误差的组合,利用主成分分析,可以将他们区分和表示出来。由于原始数据不总是正态分析,且采用了不同的数学模型,NATA方法得到的尧敦椭圆和ISO 13528得到的尧敦椭圆有时是不同的。     

基于二元多项式拟合法的压力传感器输入信号重构

为了同时解决压力传感器输出特性的非线性和温度漂移问题,提出利用二元多项式根据传感器输出信号及其内部温度来重构被测压力.给出了被测压力重构模型的具体形式,以传感器静态特性标定试验数据为依据,利用最小二乘法求解模型系数矩阵,利用单点最大拟合误差、误差平方和模型阶次三项指标进行模型择优.基于重构模型给出了测量电路检测精度估算方法.本方法在传感器静态特性标定数据范围内得到了便于工程计算的一致表达式,同时解决了传感器的非线性和温度漂移两个主要问题,计算所用数据量大大小于插值法.某型硅谐振压力传感器的应用验证了本方法的合理性和有效性.     

基于仿射变换和B样条的参数曲面变形方法

发展了一种新的参数曲面变形方法:采用一种特殊的二元B样条展开式作为变换的伸缩函数,构造了具有明确几何意义的变换矩阵,对于待变形的曲面部分,逐点施行仿射变换,B样条展开式的系数可作为变形的控制参数,每个参数具有局部可控性,可分别定量地控制变形的发生区域、变形区域边界处的连续性与光滑性、变形方向和变形幅度等。实验表明,该方法数学模型简单,计算量小,通过交互改变控制参数,可获得预期的丰富的形状修改和变形效果。适用于几何造型、计算机动画、CAD等领域。     

Bivariate models of optimism and pessimism in multi-criteria decision-making based on intuitionistic fuzzy sets

This paper presents a useful method of relating optimism and pessimism to multiple criteria decision analysis in the context of intuitionistic fuzzy sets based on the unipolar bivariate model. We use eight point operators to estimate the adaptational outcome expectations of optimism and/or pessimism and then determine the net predisposition, the aggregated effect of positive and negative evaluations. A series of new net predispositions for bivariate evaluations are proposed for neutrality; for complete, moderate, and rational optimism; for complete, moderate, and rational pessimism; and for complete and moderate optimism-pessimism. The suitability function, which measures the overall evaluation of each alternative, is then presented. Because positive or negative leniency may exist, such that most of the criteria may be assigned unduly high or low ratings, respectively, we introduce deviation variables to mitigate the effects of such ratings on the apparent importance of various criteria. Based on the two objectives of maximal weighted suitability and minimal deviation values, an integrated programming model is used to compute the optimal weights for the criteria and the corresponding degrees of suitability of the alternative rankings. We establish flexible algorithms that incorporate both objective and subjective information to compute the optimal optimistic and pessimistic decisions. The proposed methods are illustrated and discussed using a numerical example, a multi-criteria supplier selection problem. Finally, an empirical study of job choices is conducted to establish the feasibility and applicability of the current method.     

An EM algorithm for estimating the parameters of bivariate Weibull distribution under random censoring

We consider the problem of estimation of the parameters of the Marshall-Olkin Bivariate Weibull distribution in the presence of random censoring. Since the maximum likelihood estimators of the parameters cannot be expressed in a closed form, we suggest an EM algorithm to compute the same. Extensive simulations are carried out to conclude that the estimators perform efficiently under random censoring.     

Modeling bivariate long-range dependence with general phase

Bivariate time series models are considered that are suitable for estimation, that have interpretable parameters and that can capture the general semi-parametric formulation of bivariate long-range dependence, including a general phase. The models also allow for short-range dependence and fractional cointegration. A simulation study to test the performance of a conditional maximum likelihood estimation method is carried out, under the proposed models. Finally, an application is presented to the U.S. inflation rates in goods and services where models not allowing for general phase suffer from misspecification.     

一类分形插值函数的变差和计盒维数

讨论一类网格上二元连续分形插值曲面,研究二元连续函数的振幅与变差的性质。对于二元连续分形插值函数,给出了变差的估计,并根据连续函数变差与图像计盒维数之间的关系,得出了分形插值曲面计盒维数的准确值。     

一种新的二元有理插值及其性质

构造了一种带参数的仅基于函数值的分子为双四次、分母为双二次的二元有理插值样条函数,插值函数具有简洁的显式表示。插值函数中含有4个参数,当这些参数满足一定条件时,插值曲面在插值区域上C1光滑。由于插值函数中含有参数,这样可以在插值数据不变的情况下通过对参数的选择进行插值曲面的局部修改。最后讨论了插值函数的一些性质。