Using Pearson’s System of Curves to Approximate the Distributions of the Difference between Two Correlated Estimates of Signal-to-Noise Ratios: The Cases of Bivariate Normal and Bivariate Lognormal Distributions

Background: The signal-to-noise ratio (SNR) is recognized as an index of measurements reproducibility. We derive the maximum likelihood estimators of SNR and discuss confidence interval construction on the difference between two correlated SNRs when the readings are from bivariate normal and bivariate lognormal distribution. We use the Pearsons system of curves to approximate the difference between the two estimates and use the bootstrap methods to validate the approximate distributions of the statistic of interest. Methods: The paper uses the delta method to find the first four central moments, and hence the skewness and kurtosis which are important in the determination of the parameters of the Pearsons distribution. Results: The approach is illustrated in two examples;one from veterinary microbiology and food safety data and the other on data from clinical medicine. We derived the four central moments of the target statistics, together with the bootstrap method to evaluate the parameters of Pearsons distribution. The fitted Pearsons curves of Types I and II were recommended based on the available data. The R-codes are also provided to be readily used by the readers.

The Bivariate Normal Integral via Owen’s T Function as a Modified Euler’s Arctangent Series

The Owen’s T function is presented in four new ways, one of them as a series similar to the Euler’s arctangent series divided by 2π, which is its majorant series. All possibilities enable numerically stable and fast convergent computation of the bivariate normal integral with simple recursion. When tested computation on a random sample of one million parameter triplets with uniformly distributed components and using double precision arithmetic, the maximum absolute error was 3.45 × 10-16. In additional testing, focusing on cases with correlation coefficients close to one in absolute value, when the computation may be very sensitive to small rounding errors, the accuracy was retained. In rare potentially critical cases, a simple adjustment to the computation procedure was performed—one potentially critical computation was replaced with two equivalent non-critical ones. All new series are suitable for vector and high-precision computation, assuming they are supplemented with appropriate efficient and accurate computation of the arctangent and standard normal cumulative distribution functions. They are implemented by the R package Phi2rho, available on CRAN. Its functions allow vector arguments and are ready to work with the Rmpfr package, which enables the use of arbitrary precision instead of double precision numbers. A special test with up to 1024-bit precision computation is also presented.

基于Bivariate Probit模型的土地流转影响因素分析——以江西省为例

在2011年江西省农户调研数据的基础上,利用Bivariate Probit模型分析了影响农户土地流转行为的因素及土地转入转出行为之间的联立关系。计量结果显示:农户土地转入和转出行为之间存在替代效应;家庭女男比例、人均承包地面积、户主年龄及受教育年限、拥有的农业资产价值、外出务工及土地调整等是影响农户土地流转行为的重要因素。

The Cox-Aalen Models as Framework for Construction of Bivariate Probability Distributions, Universal Representation

Starting with the Aalen （1989） version of Cox （1972） ＇regression model＇ we show the method for construction of ＂any＂ joint survival function given marginal survival functions. Basically, however, we restrict ourselves to model positive stochastic dependences only with the general assumption that the underlying two marginal random variables are centered on the set of nonnegative real values. With only these assumptions we obtain nice general characterization of bivariate probability distributions that may play similar role as the copula methodology. Examples of reliability and biomedical applications are given.

基于Bivariate模型的非抽取小波域图像复原

将Bivariate模型引入到图像复原中,以Bivariate概率分布函数作为自然图像小波系数向量的先验模型。从图像复原的Bayesian理论出发,提出基于Bivariate概率分布函数非抽取小波域的图像复原算法,并从自适应规整化的角度来分析该算法的有效性。通过对4幅标准测试图像复原实验,并将该算法复原结果与其他3种人们熟知的图像复原算法效果进行对比来证明该算法的有效性。

EXISTENCE AND LOCAL BEHAVIOR OF NONDIAGONAL BIVARIATE QUADRATIC FUNCTION APPROXIMATION

This paper analyses the local behavior of the simple off-diagonal bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin.It is shown that the simple off-diagonal bivariate quadratic Hermite-Padé form always defines a bivariate quadratic function and that this function is analytic in a neighbourhood of the origin.Numerical examples compare the obtained results with the approximation power of diagonal Chisholm approximant and Taylor polynomial approximant.

The Existence and Local Behavior of the Bivariate Quadratic Function Approximation

This paper analysis the local behavior of the bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin. It is shown that the bivariate quadratic Hermite-Padé form always defines a bivariate quadratic function and that this function is analytic in a neighborhood of the origin.

GLOBAL SMOOTHNESS PRESERVATION BY BIVARIATE INTERPOLATION OPERATORS

Extending the results of [4] in the univariate case, in this paper we prove that the bivariate interpolation polynomials of Hermite-Fejér based on the Chebyshev nodes of the first kind, those of Lagrange based on the Chebyshev nodes of second kind and ±1, and those of bivariate Shepard operators, have the property of partial preservation of global smoothness, with respect to various bivariate moduli of continuity.

On Characterization of Poised Nodes for a Space of Bivariate Functions

There are several examples of spaces of univariate functions for which we have a characterization of all sets of knots which are poised for the interpolation problem. For the standard spaces of univariate polynomials, or spline functions the mentioned results are well-known. In contrast with this, there are no such results in the bivariate case. As an exception, one may consider only the Pascal classic theorem, in the interpolation theory interpretation. In this paper, we consider a space of bivariate piecewise linear functions, for which we can readily find out whether the given node set is poised or not. The main tool we use for this purpose is the reduction by a basic subproblem, introduced in this paper.

GIS-based landslide susceptibility mapping using numerical risk factor bivariate model and its ensemble with linear multivariate regression and boosted regression tree algorithms

In this study, a novel approach of the landslide numerical risk factor(LNRF) bivariate model was used in ensemble with linear multivariate regression(LMR) and boosted regression tree(BRT) models, coupled with radar remote sensing data and geographic information system(GIS), for landslide susceptibility mapping(LSM) in the Gorganroud watershed, Iran. Fifteen topographic, hydrological, geological and environmental conditioning factors and a landslide inventory(70%, or 298 landslides) were used in mapping. Phased array-type L-band synthetic aperture radar data were used to extract topographic parameters. Coefficients of tolerance and variance inflation factor were used to determine the coherence among conditioning factors. Data for the landslide inventory map were obtained from various resources, such as Iranian Landslide Working Party(ILWP), Forestry, Rangeland and Watershed Organisation(FRWO), extensive field surveys, interpretation of aerial photos and satellite images, and radar data. Of the total data, 30% were used to validate LSMs, using area under the curve(AUC), frequency ratio(FR) and seed cell area index(SCAI).Normalised difference vegetation index, land use/land cover and slope degree in BRT model elevation, rainfall and distance from stream were found to be important factors and were given the highest weightage in modelling. Validation results using AUC showed that the ensemble LNRF-BRT and LNRFLMR models(AUC = 0.912(91.2%) and 0.907(90.7%), respectively) had high predictive accuracy than the LNRF model alone(AUC = 0.855(85.5%)). The FR and SCAI analyses showed that all models divided the parameter classes with high precision. Overall, our novel approach of combining multivariate and machine learning methods with bivariate models, radar remote sensing data and GIS proved to be a powerful tool for landslide susceptibility mapping.

Residual life estimation based on bivariate Wiener degradation process with measurement errors

An adaptive method of residual life estimation for deteriorated products with two performance characteristics (PCs) was proposed, which was sharply different from existing work that only utilized one-dimensional degradation data. Once new degradation information was available, the residual life of the product being monitored could be estimated in an adaptive manner. Here, it was assumed that the degradation of each PC over time was governed by a Wiener degradation process and the dependency between them was characterized by the Frank copula function. A bivariate Wiener process model with measurement errors was used to model the degradation measurements. A two-stage method and the Markov chain Monte Carlo (MCMC) method were combined to estimate the unknown parameters in sequence. Results from a numerical example about fatigue cracks show that the proposed method is valid as the relative error is small.

BIVARIATE BLENDING RATIONAL INTERPOLANTS

Both the Newton interpolating polynomials and the Thiele-type interpolating continued fractions based on inverse differences are used to construct a kind of bivariate blending rational interpolants and an error estimation is given.

Bayesian framework for satellite rechargeable lithium battery synthesizing bivariate degradation and lifetime data

Reliability and remaining useful life(RUL)estimation for a satellite rechargeable lithium battery(RLB)are significant for prognostic and health management(PHM).A novel Bayesian framework is proposed to do reliability analysis by synthesizing multisource data,including bivariate degradation data and lifetime data.Bivariate degradation means that there are two degraded performance characteristics leading to the failure of the system.First,linear Wiener process and Frank Copula function are used to model the dependent degradation processes of the RLB's temperature and discharge voltage.Next,the Bayesian method,in combination with Markov Chain Monte Carlo(MCMC)simulations,is provided to integrate limited bivariate degradation data with other congeneric RLBs'lifetime data.Then reliability evaluation and RUL prediction are carried out for PHM.A simulation study demonstrates that due to the data fusion,parameter estimations and predicted RUL obtained from our model are more precise than models only using degradation data or ignoring the dependency of different degradation processes.Finally,a practical case study of a satellite RLB verifies the usability of the model.

Inference for dependence competing risks from bivariate exponential model under generalized progressive hybrid censoring with partially observed failure causes

Inference are considered for the dependence competing risks model by using the Marshal-Olkin bivariate exponential distribution. Under generalized progressively hybrid censoring with partially observed failure causes, the maximum likelihood estimators are established, and the approximate confidence intervals are also constructed via the observed Fisher information matrix.Moreover, Bayes estimates and highest probability density credible intervals are presented and the importance sampling technique is used to compute corresponding results. Finally, the numerical analysis is proposed for illustration.

THE INSTABILITY DEGREE IN THE DIEMNSION OF SPACES OF BIVARIATE SPLINE

In this paper, the dimension of the spaces of bivariate spline with degree less that 2r and smoothness order r on the Morgan-Scott triangulation is considered. The concept of the instability degree in the dimension of spaces of bivariate spline is presented. The results in the paper make us conjecture the instability degree in the dimension of spaces of bivariate spline is infinity.

Reliability modeling of the bivariate deteriorating product with both monotonic and non-monotonic degradation paths

Fiber optical gyroscope(FOG)is a highly reliable navigation element,and the degradation trajectories of its two accuracy indexes are monotonic and non-monotonic respectively.In this paper,a flexible accelerated degradation testing(ADT)model is used for analyzing the bivariate dependent degradation process of FOG.The time-varying copulas are employed to consider the dynamic dependency structure between two marginal degradation processes as the Wiener process and the inverse Gaussian process.The statistical inference is implemented by utilizing an inference function for the margins(IFM)approach.It is demonstrated that the proposed method is powerful in modeling the joint distribution with various margins.

MATRIX ALGORITHMS AND ERROR FORMULA FOR BIVARIATE THIELE-TYPE RECTANGULAR MATRIX VALUED RATIONAL INTERPOLATION

A new method for the construction of bivariate matrix valued rational interpolants (BGIRI) on a rectangular grid is presented in [6]. The rational interpolants are of Thiele-type continued fraction form with scalar denominator. The generalized inverse introduced by [3]is gen-eralized to rectangular matrix case in this paper. An exact error formula for interpolation is ob-tained, which is an extension in matrix form of bivariate scalar and vector valued rational interpola-tion discussed by Siemaszko[l2] and by Gu Chuangqing [7] respectively. By defining row and col-umn-transformation in the sense of the partial inverted differences for matrices, two type matrix algorithms are established to construct corresponding two different BGIRI, which hold for the vec-tor case and the scalar case.

Rotational nanofluids for oxytactic microorganisms with convective boundary conditions using bivariate spectral quasi-linearization method

In this study,we considered the three-dimensional flow of a rotating viscous,incompressible electrically conducting nanofluid with oxytactic microorganisms and an insulated plate floating in the fluid.Three scenarios were considered in this study.The first case is when the fluid drags the plate,the second is when the plate drags the fluid and the third is when the plate floats on the fluid at the same velocity.The denser microorganisms create the bioconvection as they swim to the top following an oxygen gradient within the fluid.The velocity ratio parameter plays a key role in the dynamics for this flow.Varying the parameter below and above a critical value alters the dynamics of the flow.The Hartmann number,buoyancy ratio and radiation parameter have a reverse effect on the secondary velocity for values of the velocity ratio above and below the critical value.The Hall parameter on the other hand has a reverse effect on the primary velocity for values of velocity ratio above and below the critical value.The bioconvection Rayleigh number decreases the primary velocity.The secondary velocity increases with increasing values of the bioconvection Rayleigh number and is positive for velocity ratio values below 0.5.For values of the velocity ratio parameter above 0.5,the secondary velocity is negative for small values of bioconvection Rayleigh number and as the values increase,the flow is reversed and becomes positive.

Generating function of product of bivariate Hermite polynomials and their applications in studying quantum optical states

By virtue of the operator-Hermite-polynomial method, we derive some new generating function formulas of the product of two bivariate Hermite polynomials. Their applications in studying quantum optical states are presented.

An Extended Bivariate T-Distribution Type Symmetry Model for Square Contingency Tables

The purpose of this paper is to propose a new model of asymmetry for square contingency tables with ordered categories. The new model may be appropriate for a square contingency table if it is reasonable to assume an underlying bivariate t-distribution with different marginal variances having any degrees of freedom. As the degrees of freedom becomes larger, the proposed model approaches the extended linear diagonals-parameter symmetry model, which may be appropriate for a square table if it is reasonable to assume an underlying bivariate normal distribution. The simulation study based on bivariate t-distribution is given. An example is given.