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 ...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.展开更多
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 ...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<sup>-</sup><sup>16</sup>. 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.展开更多
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 s...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.展开更多
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 re...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.展开更多
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 estima...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.展开更多
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,...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.展开更多
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 degra...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.展开更多
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) c...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.展开更多
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 de...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.展开更多
文摘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.
文摘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<sup>-</sup><sup>16</sup>. 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.
基金Under the auspices of the National Social Science Found of China(No.21XGL019)Hainan Provincial Natural Science Foundation of China(No.421RC1034)Professor/Doctor Research Foundation of Huizhou University(No.2022JB080)。
文摘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.
基金supported by the Centre for Advanced Modelling and Geospatial Information Systems(CAMGIS),UTS under grant numbers 321740.2232335,323930,and 321740.2232357
文摘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.
文摘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.
基金supported by the National Natural Science Foundation of China(11501433)the Fundamental Research Funds for the Central Universities(JB180711)
文摘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.
基金Project(60904002)supported by the National Natural Science Foundation of China
文摘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.
基金Supported by the National Natural Science Foundation of China(No.41406146)the Laboratory for Marine Fisheries Science and Food Production Processes at Qingdao National Laboratory for Marine Science and Technology of China(No.2017-1A02)the Shanghai Universities First-class Disciplines Project-Fisheries(A)
文摘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.
文摘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.