Quadratic Radical Function Better Than Fisher z Transformation

A new explicit quadratic radical function is found by numerical experiments,which is simpler and has only 70.778%of the maximal distance error compared with the Fisher z transformation.Furthermore,a piecewise function is constructed for the standard normal distribution:if the independent variable falls in the interval(-1.519,1.519),the proposed function is employed;otherwise,the Fisher z transformation is used.Compared with the Fisher z transformation,this piecewise function has only 38.206%of the total error.The new function is more exact to estimate the confidence intervals of Pearson product moment correlation coefficient and Dickinson best weights for the linear combination of forecasts.

STRONG REPRESENTATIONS OF THE SURVIVAL FUNCTION ESTIMATOR ON INCREASING SETS FOR TRUNCATED AND CENSORED DATA

In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. which are valid up to a given order statistic of the observations. A precise bound for the errors is obtained which only depends on the index of the last order statistic to be included.

Developing Weibull-based diameter distributions for the major coniferous species in Heilongjiang Province,China

Diameter distribution models play an important role in forest inventories,growth prediction,and management.The Weibull probability density function is widely used in forestry.Although a number of methods have been proposed to predict or recover the Weibull distribution,their applicability and predictive performance for the major tree species of China remain to be determined.Trees in sample plots of three even-aged coniferous species(Larix olgensis,Pinus sylvestris and Pinus koraiensis)were measured both in un-thinned and thinned stands to develop parameter prediction models for the Weibull probability density function.Ordinary least squares(OLS)and maximum likelihood regression(MLER),as well as cumulative distribution function regression(CDFR)were used,and their performance compared.The results show that MLER and CDFR were better than OLS in predicting diameter distributions of tree plantations.CDFR produced the best results in terms of fitting statistics.Based on the error statistics calculated for different age groups,CDFR was considered the most suitable method for developing prediction models for Weibull parameters in coniferous plantations.

The New Mixed Generalized Erlang Distribution

In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by wi ≥ 0 and . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by wi ∈ R, and maintaining . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.

Application of saddlepoint approximation in reliability analysis of dynamic systems

The application of the saddlepoint approximation to reliability analysis of dynamic systems is investigated. The failure event in reliability problems is formulated as the exceedance of a single performance variable over a prescribed threshold level. The saddlepoint approximation technique provides a choice to estimate the cumulative distribution function （CDF） of the performance variable. The failure probability is obtained as the value of the complement CDF at a specified threshold. The method requires computing the saddlepoint from a simple algebraic equation that depends on the cumulant generating function （CGF） of the performance variable. A method for calculating the saddlepoint using random samples of the performance variable is presented. The applicable region of the saddlepoint approximation is discussed in detail. A 10-story shear building model with white noise excitation illustrates the accuracy and efficiency of the proposed methodology.

Utilizing a new soil effective temperature scheme and archived satellite microwave brightness temperature data to estimate surface soil moisture in the Nagqu region, Tibetan Plateau of China

Since the early 2000s, many satellite passive microwave brightness temperature （BT） archives, such as the Advanced Microwave Scanning Radiometer for the Earth Observing System （AMSR-E） BTs, have become the useful resources for assessing the changes in the surface and deep soil moistures over both arid and semi-arid regions. In this study, we used a new soil effective temperature （T scheme and the archived AMSR-E BTs to estimate surface soil moisture （SM） over the Nagqu region in the central Tibetan Plateau, China. The surface and deep soil temperatures required for the calculation of regional-scale T were obtained from outputs of the Community Land Model version 4.5 （CLM4.5）. In situ SM measurements at the CEOP-CAMP/Tibet （Coordinated Enhanced Observing Period Asia-Australia Monsoon Project on the Tibetan Plateau） experimental sites were used to validate the AMSR-E-based SM estimations at regional and single-site scales. Furthermore, the spatial distribution of monthly mean surface SM over the Nagqu region was obtained from 16 daytime AMSR-E BT observations in July 2004 over the Nagqu region. Results revealed that the AMSR-E-based surface SM estimations agreed well with the in situ-based surface SM measurements, with the root mean square error （RMSE） ranging from 0.042 to 0.066 m3/m3 and the coefficient of determination （R2） ranging from 0.71 to 0.92 during the nighttime and daytime. The regional surface soil water state map showed a clear spatial pattern related to the terrain. It indicated that the lower surface SM values occurred in the mountainous areas of the northern, mid-western and southeastern parts of Nagqu region, while the higher surface SM values appeared in the low elevation areas such as the Tongtian River Basin, Namco Lake and bog meadows in the central part of Nagqu region. Our analysis also showed that the new T^scheme does not require special fitting parameters or additional assumptions, which simplifies the data requirements for regional-scale applications. This scheme combined with the archived satellite passive microwave BT observations can be used to estimate the historical surface SM for hydrological process studies over the Tibetan Plateau regions.

Cogging Torque Sensitivity considering Imperfect Magnet Positioning for Permanent Magnet Machines of Different Slot and Pole Count

This work is about analyzing surface mounted permanent magnet machines regarding their sensitiveness related to erroneous magnet positioning.A finite element analysis based approach is presented and different topologies in terms of slot and pole count are compared.The study further includes the analysis of multiple magnet widths and stator teeth widths.By contrast to most of previous studies,the work is based on evaluating the cumulative distribution function of the cogging torque in case of non-idealities.A Monte Carlo importance sampling based strategy is focused.This approach facilitates studying arbitrary tolerance distributions.Results reveal that topologies with particularly promising rated cogging torque behaviour exhibit the most significant performance degradation in presence of tolerances.A linear relationship is identified for cogging torque performance as function of the accuracy in magnet positioning.Results emphasize the necessity of tolerance analyses for electric machine design to not overrate their performance in the presence of manufacturing uncertainties.

The empirical relationships between M_S,m_band M_L for China and vicinity

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Consistency of the Estimator of Cumulative Hazard Function in Estimated Pseudo-Partial-Likelihood Approach

For multivariate failure time with auxiliary covariate information, an estimated pseudo-partial-likelihood estimator under the marginal hazard model with distinguishable baseline hazard has been proposed. However, the asymptotic properties of the corresponding estimated cumulative hazard function have not been studied. In this paper, based on counting process martingale, we use the continuous mapping theorem and Lenglart inequality and prove the consistency of the estimated cumulative hazard function in estimated pseudo-partial-likelihood approach.

Load distributions of some classic DHTs

The load balance is a critical issue of distributed Hash table （DHT）, and the previous work shows that there exists O（logn） imbalance of load in Chord. The load distribution of Chord, Pastry, and the virtual servers （VS） balancing scheme and deduces the closed form expressions of the probability density function （PDF） and cumulative distribution function （CDF） of the load in these DHTs is analyzes. The analysis and simulation show that the load of all these DHTs obeys the gamma distribution with similar formed parameters.

Uncertainties in estimation of extrapolated annual occurence rate of earthquakes using logical tree

he logical tree methods are used for evaluate quantitatively relationship between frequency and magnitude, and deduce uncertainties of annual occurrence rate of earthquakes in the periods of lower magnitude earthquake. The uncertainties include deviations from the self-similarity of frequency-magnitude relations, different fitting methods, different methods obtained the annual occurrence rate, magnitude step used in fitting, start magnitude, error of magnitude and so on. Taking Xianshuihe River source zone as an example, we analyze uncertainties of occurrence rate of earthquakes M4, which is needed in risk evaluation extrapolating from frequency-magnitude relations of stronger earthquakes. The annual occurrence rate of M4 is usually required for seismic hazard assessment.The sensitivity analysis and examinations indicate that, in the same frequencymagnitude relations fitting method, the most sensitive factor is annual occurrence rate, the second is magnitude step and the following is start magnitude. Effect of magnitude error is rather small.Procedure of estimating the uncertainties is as follows:①Establishing a logical tree described uncertainties in frequencymagnitude relations by available data and knowledge about studied region.② Calculating frequencymagnitude relations for each end branches. ③ Examining sensitivities of each uncertainty factors, amending structure of logical tree and adjusting original weights. ④ Recalculating frequencymagnitude relations of end branches and complementary cumulative distribution function (CCDF) in each magnitude intervals.⑤ Obtaining an annual occurrence rate of M4 earthquakes under given fractiles.Taking fractiles as 20% and 80%, annual occurrence rate of M 4 events in Xianshuihe seismic zone is 0.643 0. The annual occurrence rate is 0.631 8 under fractiles of 50%, which is very close to that under fractiles 20% and 80%.

Solving Schrodinger Equation with Soft Constrained Monotonic Neural Network

Artificial Neural Network(ANN)has become a powerful tool in the field of scientific research with its powerful information encapsulation ability and convenient variational optimization method.In particular,there have been many recent advances in computational physics to solve variational problems.Deep Neural Network(DNN)is used to represent the wave function to solve quantum many-body problems using variational optimization.In this work we used a new Physics-Informed Neural Network(PINN)to represent the Cumulative Distribution Function(CDF)of some classical problems in quantum mechanics and to obtain their ground state wave function and ground state energy through the CDF.By benchmarking against the exact solution,the error of the results can be controlled at a very low level.This new network architecture and optimization method can provide a new choice for solving quantum many-body problems.

LOCAL POLYNOMIAL DOUBLE-SMOOTHING ESTIMATION OF A CONDITIONAL DISTRIBUTION FUNCTION WITH DEPENDENT

Based on the idea of local polynomial double-smoother, we propose an estimator of a conditional cumulative distribution function with dependent and left-truncated data. It is assumed that the observations form a stationary a-mixing sequence. Asymptotic normality of the estimator is established. The finite sample behavior of the estimator is investigated via simulations.

Solving Schrodinger equations using a physically constrained neural network

Deep neural networks(DNNs)and auto differentiation have been widely used in computational physics to solve variational problems.When a DNN is used to represent the wave function and solve quantum many-body problems using variational optimization,various physical constraints have to be injected into the neural network by construction to increase the data and learning efficiency.We build the unitary constraint to the variational wave function using a monotonic neural network to represent the cumulative distribution function(CDF)F(x)=ʃ^(x)_(-∞)Ψ*Ψdx',.Using this constrained neural network to represent the variational wave function,we solve Schrodinger equations using auto-differentiation and stochastic gradient descent(SGD)by minimizing the violation of the trial wave function(x)to the Schrodinger equation.For several classical problems in quantum mechanics,we obtain their ground state wave function and energy with very low errors.The method developed in the present paper may pave a new way for solving nuclear many-body problems in the future.

The CDF and its sensitivity analysis of stochastic structure with stochastic excitation by advanced stratified line sampling

For the stochastic structure with stochastic excitation, an advanced stratified line sampling (SLS) method is presented to obtain the cumulative distribution function (CDF) of the structural response and its sensitivity. The advanced stratified line sampling method introduces a set of middle failure subsets firstly. And for each subset, the conventional line sampling can be used to obtain the corresponding value of the response's CDF. At the same time, the sensitivity estimations of each failure subset can also be computed by modifying the important direction and corresponding reliability coefficients. The properties of CDF sensitivity are proved while the performance function is linear with normal random variables. After two simple examples are used to demonstrate the properties of CDF sensitivity and the feasibility of the presented method, the method employed to analyze the CDF and corresponding sensitivity of root bending moment (RBM) responses for the stochastic BAH is wing with gust excitation to a square-edged gust and to a Dryden gust. The results show that the parameters of the second and the fifth order modals exert more influence on the CDF of response than the other ones, and the presented SLS method can more significantly reduce the computational cost compared with Monte Carlo simulation (MCS).

The cooperative and conflictual interactions between the United States,Russia,and China:A quantitative analysis of event data

The United States,Russia and China are militarily and economically among the most powerful countries in the post-Cold War period,and the interactions between the three powers heavily influence the international system.However,different conclusions about this question are generally made by researchers through qualitative analysis,and it is necessary to objectively and quantitatively investigate their interactions.Monthly-aggregated event data from the Global Data on Events,Location and Tone(GDELT)to measure cooperative and conflictual interactions between the three powers,and the complementary cumulative distribution function(CCDF)and the vector autoregression(VAR)method are utilized to investigate their interactions in two periods:January,1991 to September,2001,and October,2001 to December,2016.The results of frequencies and strengths analysis showed that:the frequencies and strengths of USA-China interactions slightly exceeded those of USA-Russia interactions and became the dominant interactions in the second period.Although that cooperation prevailed in the three dyads in two periods,the conflictual interactions between the USA and Russia tended to be more intense in the second period,mainly related to the strategic contradiction between the USA and Russia,especially in Georgia,Ukraine and Syria.The results of CCDF indicated that similar probabilities in the cooperative behaviors between the three dyads,but the differences in the probabilities of conflictual behaviors in the USA-Russia dyad showed complicated characteristic,and those between Russia and China indicated that Russia had been consistently giving China a hard time in both periods when dealing with conflict.The USA was always an essential factor in affecting the interactions between Russia and China in both periods,but China’s behavior only played a limited role in influencing the interactions between the USA-Russia dyad.Our study provides quantitative insight into the direct cooperative and conflictual interactions between the three dyads since the end of the Cold War and helps to understand their interactions better.

Mortality of Amur tigers:The more things change,the more they stay the same

Poaching as well as loss of habitat and prey are identified as causes of tiger population declines.Although some studies have examined habitat requirements and prey availability,few studies have quantified cause-specific mortality of tigers.We used cumulative incidence functions(CIFs)to quantify cause-specific mortality rates of tigers,expanding and refining earlier studies to assess the potential impact of a newly emerging disease.To quantify changes in tiger mortality over time,we re-examined data first collected by Goodrich et al.(2008;study period 1:1992–2004)as well as new telemetry data collected since January 2005(study period 2:2005–2012)using a total of 57 tigers(27 males and 30 females)monitored for an average of 747 days(range 26–4718 days).Across the entire study period(1992 to 2012)we found an estimated average annual survival rate of 0.75 for all tigers combined.Poaching was the primary cause of mortality during both study periods,followed by suspected poaching,distemper and natural/unknown causes.Since 2005,poaching mortality has remained relatively constant and,if combined with suspected poaching,may account for a loss of 17–19%of the population each year.Canine distemper virus(CDV)may be an additive form of mortality to the population,currently accounting for an additional 5%.Despite this relatively new source of mortality,poaching remains the main threat to Amur tiger survival and,therefore,population growth.

Regional moment-independent sensitivity analysis with its applications in engineering

Traditional Global Sensitivity Analysis（GSA） focuses on ranking inputs according to their contributions to the output uncertainty.However,information about how the specific regions inside an input affect the output is beyond the traditional GSA techniques.To fully address this issue,in this work,two regional moment-independent importance measures,Regional Importance Measure based on Probability Density Function（RIMPDF） and Regional Importance Measure based on Cumulative Distribution Function（RIMCDF）,are introduced to find out the contributions of specific regions of an input to the whole output distribution.The two regional importance measures prove to be reasonable supplements of the traditional GSA techniques.The ideas of RIMPDF and RIMCDF are applied in two engineering examples to demonstrate that the regional moment-independent importance analysis can add more information concerning the contributions of model inputs.

An Additive-Multiplicative Cox-Aalen Subdistribution Hazard Model for Competing Risks Data

This paper proposes a flexible additive-multiplicative Cox-Aalen hazard model which allows time-varying covariate effects for the subdistribution in a competing risks study.Weigh ted estimating equation approaches under an covariates-dependent adjusted weight by fitting the Cox proportional hazard model for the censoring distribution are established for inference on the model parametric and nonparametric components.In addition,large number properties are presented and the finite sample behavior of the proposed estimators is evaluated through simulation studies,estimators from the proposed method perform satisfactorily on reduction of the bias.The authors apply our model to a competing risks data set from a tamoxifen trail for breast cancer study.

Study on Ensemble-Based Forecast of Extremely Heavy Rainfalls in China: Experiments for July 2011 Cases

According to the Anderson-Darling principle, a method for forecast of extremely heavy rainfall （abbre- viated as extreme rainfall/precipitation） was developed based on the ensemble forecast data of the T213 global ensemble prediction system （EPS） of the China Meteorological Administration （CMA）. Using the T213 forecast precipitation data during 2007-2010 and the observed rainfall data in June-August of 2001 2010, characteristics of the cumulative distribution functions （CDFs） of the observed and the T213 EPS forecast precipitation were analyzed. Accordingly, in the light of the continuous differences of the CDFs between model climate and EPS forecasts, a mathematical model of Extreme Precipitation Forecast Index （EPFI） was established and applied to forecast experiments of several extreme rainfall events in China during 17-31 July 2011. The results show that the EPFI has taken advantage of the tail information of the model climatic CDF and provided agreeable forecasts of extreme rainfalls. The EPFI based on the T213 EPS is useful for issuing early warnings of extreme rainfalls 3 7 days in advance. With extension of the forecast lead time, the EPFI becomes less skillful. The results also demonstrate that the rationality of the model climate CDF was of vital importance to the skill of EPFI.