Uniformly Minimum-Variance Unbiased Estimator (UMVUE) for the Gamma Cumulative Distribution Function with Known and Integer Scale Parameter

Uniformly minimum-variance unbiased estimator (UMVUE) for the gamma cumulative distribution function with known and integer scale parameter. This paper applies Rao-Blackwell and Lehmann-Scheffeé Theorems to deduce the uniformly minimum-variance unbiased estimator (UMVUE) for the gamma cumulative distribution function with known and integer scale parameters. The paper closes with an example comparing the empirical distribution function with the UMVUE estimates.

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.

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.

Seismic loss assessment of RC high-rise buildings designed according to Eurocode 8

A probabilistic seismic loss assessment of RC high-rise(RCHR)buildings designed according to Eurocode 8 and located in the Southern Euro-Mediterranean zone is presented herein.The loss assessment methodology is based on a comprehensive simulation approach which takes into account ground motion(GM)uncertainty,and the random effects in seismic demand,as well as in predicting the damage states(DSs).The methodology is implemented on three RCHR buildings of 20-story,30-story and 40-story with a core wall structural system.The loss functions described by a cumulative lognormal probability distribution are obtained for two intensity levels for a large set of simulations(NLTHAs)based on 60 GM records with a wide range of magnitude(M),distance to source(R)and different site soil conditions(SS).The losses expressed in percent of building replacement cost for RCHR buildings are obtained.In the estimation of losses,both structural(S)and nonstructural(NS)damage for four DSs are considered.The effect of different GM characteristics(M,R and SS)on the obtained losses are investigated.Finally,the estimated performance of the RCHR buildings are checked to ensure that they fulfill limit state requirements according to Eurocode 8.

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.

A Hybrid Statistical-Dynamical Downscaling of Air Temperature over Scandinavia Using the WRF Model

An accurate simulation of air temperature at local scales is crucial for the vast majority of weather and climate applications.In this work,a hybrid statistical–dynamical downscaling method and a high-resolution dynamical-only downscaling method are applied to daily mean,minimum and maximum air temperatures to investigate the quality of localscale estimates produced by downscaling.These two downscaling approaches are evaluated using station observation data obtained from the Finnish Meteorological Institute over a near-coastal region of western Finland.The dynamical downscaling is performed with the Weather Research and Forecasting(WRF)model,and the statistical downscaling method implemented is the Cumulative Distribution Function-transform(CDF-t).The CDF-t is trained using 20 years of WRF-downscaled Climate Forecast System Reanalysis data over the region at a 3-km spatial resolution for the central month of each season.The performance of the two methods is assessed qualitatively,by inspection of quantile-quantile plots,and quantitatively,through the Cramer-von Mises,mean absolute error,and root-mean-square error diagnostics.The hybrid approach is found to provide significantly more skillful forecasts of the observed daily mean and maximum air temperatures than those of the dynamical-only downscaling(for all seasons).The hybrid method proves to be less computationally expensive,and also to give more skillful temperature forecasts(at least for the Finnish near-coastal region).

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

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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%.

Late Quaternary Slip Behavior of the Jinqianghe Fault in the Middle Qilian-Haiyuan Fault Zone,Northeastern Tibetan Plateau

The Qilian-Haiyuan fault zone in the northeastern Tibetan Plateau has been the source of strong earthquakes in the region.In its middle segment,the Jinqianghe fault is an important active fault within the Tianzhu seismic gap;however,little is known about its slip behavior.To present a new horizontal displacement distribution along this fault,we used WorldView-2 stereo pairs and unmanned aerial vehicle-based photogrammetry to construct digital elevation models to obtain a detailed tectono-geomorphic interpretation and geomorphic offsets.The offset marker measurements yielded 135 geomorphic displacements and 8 offset clusters.Radiocarbon dating was used to establish the regional age sequence of the geomorphic units in offset fluvial terraces at four study sites.The displacements and ages linked the offset clusters with the geomorphic unit sequence;the Holocene strike-slip rate of the Jinqianghe fault was estimated to 4.8-5.6 mm/a at~4-12 ka and 2.9-4.7 mm/a from~4 ka.Three recent earthquakes(with a recurrence interval of~1000 years)represent an active seismic period,revealing the potential seismic hazard along this fault because it has not ruptured in the last 1500 years.

Extracting classification rules based on a cumulative probability distribution approach

This paper deals with a reinforced cumulative probability distribution approach (CPDA) based method for extracting classification rules.The method includes two phases:(1) automatic generation of the membership function,and (2) use of the corresponding linguistic data to extract classification rules.The proposed method can determine suitable interval boundaries for any given dataset based on its own characteristics,and generate the fuzzy membership functions automatically.Experimental results show that the proposed method surpasses traditional methods in accuracy.

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.

中美俄合作与冲突互动——基于事件数据的定量分析

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.

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.

Comparative fish community structure among different types of enclosures of estuarine environments

This study explores the differences of fish assemblages in three macrotidal estuaries of Man-gyeong River Estuary(MRE),Geum River Estuary(GRE),and Han River Esturay(HRE)with similar ranges of seasonal water temperature that are diked with different levels of disconnection from freshwater discharge.The distribution of major species in the three estuaries could generally be grouped into three distinctive patterns based on their cumulative distribution with respect to the salinity gradient.The MRE was geographically closer to the GRE than to the HRE,but the fish community of the MRE more closely resembled that of the HRE.Increased freshness of the water inside the dike and the limit of coastal fish to the river may have led to this result.The results provide clues to how enclosure patterns of estuarine waters could affect fish communities over a long-term period.In addition,the information may provide guidance for how a fish community may return once environmental conditions are restored.

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.

Estimation of 1-dimensional nonlinear stochastic differential equations based on higher-order partial differential equation numerical scheme and its application

A method based on higher-order partial differential equation （PDE） numerical scheme are proposed to obtain the transition cumulative distribution function （CDF） of the diffusion process （numerical differentiation of the transition CDF follows the transition probability density function （PDF））, where a transformation is applied to the Kolmogorov PDEs first, then a new type of PDEs with step function initial conditions and 0, 1 boundary conditions can be obtained. The new PDEs are solved by a fourth-order compact difference scheme and a compact difference scheme with extrapolation algorithm. After extrapolation, the compact difference scheme is extended to a scheme with sixth-order accuracy in space, where the convergence is proved. The results of the numericM tests show that the CDF approach based on the compact difference scheme to be more accurate than the other estimation methods considered; however, the CDF approach is not time-consuming. Moreover, the CDF approach is used to fit monthly data of the Federal funds rate between 1983 and 2000 by CKLS model.