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Moran's I的广东省农用地利用空间相关分析

基于管控耕地“非粮化”背景,对广东省县域农用地利用空间相关性进行分析,以揭示各类农用地空间分布特征,为差异化耕地用途管制施策提供数据基础。利用2009—2018年广东省农用地利用现状面板数据,以县区为统计单元,利用空间自相关分析法,得出广东省122个县区2009、2013、2018年的农用地利用时空格局变化情况。结果显示:耕地、园地、林地及其他农用地面积的Moran's I指数反映出计算值保持一个较高的水平且非常显著,耕地0.36~0.40、园地0.37~0.39、林地0.37~0.38、其他农用地0.20,表明各县区4种地类面积存在较显著的空间正相关关系,广东省各类农用地(除草地)面积有着明显的空间聚集性。耕地、园地面积出现“高/高聚类”的县区主要在粤西部分地区,耕地、林地面积出现“低/低聚类”的县区主要在珠三角核心地区和粤东部分地区,园地出现“低/低聚类”的县区主要在珠三角部分地区和粤北部分地区。总体而言,广东省县域的各类农用地利用在空间分布上呈显著空间自相关特征和空间聚集特征。

Influence of Human Activity Intensity on Habitat Quality in Hainan Tropical Rainforest National Park,China

Due to long-term human activity interference,the Hainan Tropical Rainforest National Park(HTRNP)of China has experienced ecological problems such as habitat fragmentation and biodiversity loss,and with the expanding scope and intensity of human activity impact,the regional ecological security is facing serious challenges.A scientific assessment of the interrelationship between human activity intensity and habitat quality in the HTRNP is a prerequisite for achieving effective management of ecological disturbances caused by human activities and can also provide scientific strategies for the sustainable development of the region.Based on the land use change data in 2000,2010,and 2020,the spatial and temporal variations and the relationship between habitat quality(HQ)and human activity intensity(HAI)in the HTRNP were explored using the integrated valuation of ecosystem services and trade-offs(InVEST)model.System dynamics and land use simulation models were also combined to conduct multi-scenario simulations of their relationships.The results showed that during 2000–2020,the habitat quality of the HTRNP improved,the intensity of human activities decreased each year,and there was a negative correlation between the two.Second,the system dynamic model could be well coupled with the land use simulation model by combining socio-economic and natural factors.The simulation scenarios of the coupling model showed that the harmonious development(HD)scenario is effective in curbing the increasing trend of human activity intensity and decreasing trend of habitat quality,with a weaker trade-off between the two compared with the baseline development(BD)and investment priority oriented(IPO)scenarios.To maintain the authenticity and integrity of the HTRNP,effective measures such as ecological corridor construction,ecological restoration,and the implementation of ecological compensation policies need to be strengthened.

基于地图API的公共绿地可达性分析

公共绿地的可达性是评价绿色基础设施配置合理性的重要指标,能直观表征市民获取、享受绿地的便捷程度与机会。在可达性分析中引入地图API服务,基于轻量级路线规划服务结合ArcGIS构建等时圈来表征可达性,能够提高分析的直观度与精度;同时以人口密度表征片区内居民对公共绿地的需求程度,通过双变量空间自相关分析反映公共绿地供给与需求之间的匹配程度,提高评价的全面性。基于构建的可达性分析模型,以上海黄浦区淮海中路街道为例进行了实证分析,研究得出淮海中路街道绿地资源配置存在不合理性,在研究范围西南部分形成了较大面积服务盲区。同时绿地资源在空间布局上相对集中,供大过需、供小于需的供需不匹配现象明显。未来片区内公共绿地建设应以居民需求为指引,注重小尺度公共绿地的增量建设,并对利用率较低的附属绿地或公共空间进行存量提质优化。

基于时空Moran's I指数的全国降雨量自相关分析

对全国160个站点收集的1951年～2000年降雨量数据进行时空自相关分析,探讨了降雨量的时空演变特征.研究结果表明：全国降雨量呈现时空聚集特征,具有明显的时空相关性;在时间维度上,全局时空Moran＇s I指数所反映的趋势,与全国5～9月降雨量上升趋势一致,对于相邻的月份,上个月的降雨量对下个月的降雨量有直接影响,即上个月降雨高聚集的区域也很有可能是下个月降雨高聚集的区域,随着两个月之间相隔的时间越长,这种相关性逐渐减小;空间维度上,局部时空Moran＇s I指数所反映的全国降雨量聚集模式,与5～9月实际降雨空间分布相符.

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。

用Bivariate－Test方法分析温度资料的不均一性

Ｂｉｖａｒｉａｔｅ－Ｔｅｓｔ方法（以下简称Ｂ－Ｔ方法）是一种基于二维正态分布随机矢量的假设检验方法，可以在一个分量的均值不改变的前提下，检验另一分量的均值有无改变。一些气象研究工作者最早用这种方法来分析年降水量的均一性。从温度资料不均一性产生的原因看，一般可分为两类：突变型不均一及渐变型不均一。对两种类型的不均一性，我们分别推导了理想情形下Ｂ－Ｔ方法的检验结果．并用随机试验的方法分析了检验结果对资料的敏感性。以上两方面的结果表明。渐变型及突变型不均一分别对应明显不同的Ｂ－Ｔ检验结果，在实际分析中这种差异可以用来定性判断不均一性的类型。东北区２０站３０年年平均温度资料的试算结果表明，有７站资料不能通过信度９５％的Ｂ－Ｔ检验，有３站资料不能通过信度９０％的Ｂ－Ｔ检验。其中有４个站的检验结果与理想情形下渐变型不均一的检验结果相似，有４个站的检验结果与理想情形下突变型不均一的检验结果相似。有一个站存在个别点的资料错误，有一个站可能有一次以上的不均一性发生。计算结果也表明，尽管Ｂ－Ｔ方法按照理论推导只是用来检测资料的不均一性，但对个别点上的资料质量问题也有一定的检测效果。

Moran's I指数计算中空间权重文件的生成实现

Moran's I指数是空间自相关分析常用的指标。ArcGIS9.0加强了空间统计分析功能,在Moran's I指数计算中,他提供了6种空间关系的定义方法。但在基于空间权重文件的方法中,ArcGIS9.0没有提供相应的空间权重文件生成的运算工具,需编程实现。基于MapBasic实现了基于二进制权重的空间权重文件的生成,并给出了详细的实现过程和具体的应用实例。

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。

基于SPEI的贵州省气象干旱时空演变特征及双变量区域频率分析

为深入探究贵州省干旱事件发展规律及区域重现期特征,采用贵州省1960—2017年逐月气象资料计算标准化降水蒸散指数(SPEI),采用三阈值法游程理论、小波理论、Copula函数等方法对干旱时空演变特征、周期特征以及区域重现期特征进行分析。结果表明:1960—2017年贵州省干旱整体上呈严重化趋势,各分区存在差异,其中黔西南地区的干旱化趋势最为明显,SPEI线性倾向率为-0.003/10a;干旱强度由高到底的分区排序依次为黔东、黔北、黔西南、黔中、黔西北、黔南,且黔中地区的干旱发生频率最高;贵州省四季干旱的主周期分别为18、15、30和8 a,空间上南北分布差异显著,周期较长的区域范围呈现先增加后减少的趋势;贵州省黔北地区的干旱重现期最小,表明此区域发生极端干旱事件的概率较大,遭受干旱灾害的可能性较大。研究结果可为贵州省水资源管理及干旱风险防治提供科学依据。

基于改进Moran's I指数的成都市PM_(2.5)的空间统计分析

以PM2.5污染的空间分布为研究对象,改进传统Moran＇s I指数,以便适用于大样本数据的空间自相关分析。通过改进Moran＇s I指数推导出期望与方差对改进Moran＇s I指数进行统计意义上的显著性检验,从而对PM2.5污染情况进行空间自相关性的判断与评价,揭示PM2.5污染呈现的空间分布趋势。为说明改进Moran＇s I指数的实际应用价值,采用成都市区7个空气质量监测点（不包括灵岩寺监测点）PM2.5每小时数据,进行改进Moran＇s I指数的计算与分析,绘制改进全局指数时序图和改进局部Moran＇s I指数渲染图。结果表明,成都市区全局Moran＇s I指数的范围为0.728 7-0.998 5,即PM2.5污染整体呈现显著空间聚集趋势,从局部看,PM2.5污染的空间聚集和空间异质特性随着时间转移至不同监测点,地理位置邻近或环境类似的监测点有类似的分布趋势。

二元Neville型重心有理插值

基于Neville算法构造二元Neville型重心有理插值,首先把整个插值点集划分为若干子集,在子集上构造二元重心有理插值,通过Neville算法构造二元插值函数,不断重复上述过程,最终获得整个插值点集的插值函数。通过合理选择插值权,二元Neville型重心有理插值可以避免极点与不可达点的存在。

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.

Blasingame气井变产量拟稳态压降方程存在的问题及其推导与应用

稳定产量的压降曲线拟稳态法,又称为弹性二相法,可用于评价断块、岩性和裂缝系统等封闭气藏的原始地质储量,因此受到广泛的重视和应用。尤其是Blasingame提出的气井变产量拟稳态方程,受到国内外业内人士的普遍重视。本文基于达西基础单位,对变产量的拟稳态方程进行了推导和单位变换,表明了Blasingame变产量拟稳态方程存在的问题。对于低渗气藏来说,在进行井底压降曲线测试时,气井的产量难以保持稳定,而会随时间缓慢下降,因此形成了井底流压和产量同时下降的状态。对此,本文提出了双变函数的概念,并表示为J(t)=Δp(t)/qg(t)。基于双变函数提出了确定气井控制原始地质储量(OGIP)、有效渗透率和递减率的解析法和典型曲线拟合法。通过实例应用表明,两种方法评价的OGIP、有效渗透率和递减率基本一致。但解析法简单、实用、可靠,而典型曲线拟合法较为繁琐,并存在人为拟合影响的多解性。

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.

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.

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.

The impact of spatial scale on local Moran's I clustering of annual fishing effort for Dosidicus gigas offshore Peru

The spatial scale(?shing grid) of ?sheries research af fects the observed spatial patterns of?sheries resources such as catch-per-unit-ef fort(CPUE) and ?shing ef fort. We examined the scale impact of high value(HH) clusters of the annual ?shing ef fort for Dosidicus gigas of fshore Peru from 2009 to 2012.For a multi-scale analysis, the original commercial ?shery data were tessellated to twelve spatial scales from 6′ to 72′ with an interval of 6′. Under these spatial scales, D. gigas clusters were identi?ed using the Anselin Local Moran's I. Statistics including the number of points, mean CPUE, standard deviation(SD),skewness, kurtosis, area and centroid were calculated for these HH clusters. We found that the z-score of global Moran's I and the number of points for HH clusters follow a power law scaling relationship from2009 to 2012. The mean ef fort and its SD also follow a power law scaling relationship from 2009 to 2012.The skewness follows a linear scaling relationship in 2010 and 2011 but ?uctuates with spatial scale in2009 and 2012; kurtosis follows a logarithmic scale relationship in 2009, 2011 and 2012 but a linear scale relationship in 2010. Cluster area follows a power law scaling relationship in 2010 and 2012, a linear scaling relationship in 2009, and a quadratic scaling relationship in 2011. Based on the peaks of Moran's I indices and the multi-scale analysis, we conclude that the optimum scales are 12′ in 2009 ? 2011 and 6′ in 2012, while the coarsest allowable scales are 48′ in 2009, 2010 and 2012, and 60′ in 2011. Our research provides the best spatial scales for conducting spatial analysis of this pelagic species, and provides a better understanding of scaling behavior for the ?shing ef fort of D. gigas in the of fshore Peruvian waters.

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.