Methods Of Statistical Theory Research Articles

HARMONIC ANALYSISIN INVENTORY MANAGEMENT IN LOGISTICSAND SUPPLY CHAINS

The article examines the possibilities of using harmonic analysis apparatus while planning the need in stocks of various categories. The issues of improving material planning (forecasting) are currently quite relevant applied tasks in business, and are also of interest in terms of developing the theory of logistics and supply chain management. Among the approaches to planning the need for inventory, a wide range of statistical theory methods are used in practice, among which two large groups can be distinguished, such as one-parameter time series analysis models for goods of stable and relatively stable demand, as well as correlation and regression models for chaotic consumption stocks. Most of the goods sold to end consumers have a seasonal component, which may not always be explicitly expressed in statistics. However, due to change of seasons, regular fluctuations in the values of consumption from the warehouse, around the average chronological or trend, may necessitate regular recalculation of the main parameters of inventory management models, such as maximum, insurance, threshold inventory levels, etc. In addition, sales statistics may contain fluctuations of a higher order if the stocks sold have life cycles of interest in goods on the market, which can also be attributed to periodic or quasi-periodic processes. One of the methods to formalize such cyclic processes can be trigonometric approximation or harmonic analysis, when the values of a time series are represented as terms of a Fourier series (harmonics) having corresponding amplitudes and phases. The article compares the effectiveness (accuracy) of forecasts of inventory requirements made using harmonic analysis and traditional time series extrapolation methods.

The Optimization of Multimode Fiber Speckle Sensor for Microvibration

A vibration sensing system with optical fiber speckles is demonstrated and optimized with different optical fiber diameters and speckle statistical algorithms. The types of fiber diameter and material lead to a different performance of fiber specklegram sensor (FSS), which has been experimentally explored. The signal intensity, demodulated from the speckles, is different when using multimode fibers with different diameters. At the same time, the sensing effect of different fibers depends on the speckle statistical algorithms. Accordingly, we use different statistical methods in theory and experiment to analyze the influence of fiber diameter and speckle statistical methods on the sensing performance. A vibration sensing system with optimized performance is achieved by the optimized types of optical fiber and the corresponding optimized algorithms, which are promising for sensing weak vibration, such as detecting.

A comparison of spatial scan methods for cluster detection

Spatial scan methods are extremely popular for identifying disease clusters using disease count data. The original circular scan method proposed by Kulldorff [A spatial scan statistic. Comm Statist Theory Methods. 1997;26(6):1481–1496] is simple to implement, is computationally inexpensive to apply, and has high power for detecting circular clusters; however, it can struggle to identify non-circular clusters. Many extensions of the original method have been proposed to better detect irregularly-shaped clusters. We briefly describe several popular spatial scan method extensions (e.g. Upper Level Set, Flexibly-shaped, Dynamic Minimum Spanning Tree, Fast Subset, etc.). We then compare the performance of the various methods using power, sensitivity, positive predictive value, and overall accuracy by applying these methods to 126 publicly-available benchmark data sets based on 46 different cluster shapes. The comparisons go into more depth and include more methods than any previous studies of this topic; many of the methods have never been directly compared. The comprehensiveness of our study allows us to draw reliable conclusions and make concrete recommendations about the best performing methods. R packages and scripts are provided to make results reproducible.

Spatial Linear Coding in Joint Radar and Multicast Communication Systems

Introduction. This paper presents optimization methods for the amplitude-phase distribution in a transmitting antenna array in a system with a common signal for multicast data transmission and radar sensing in a given sector of space. Two approaches are considered for the choice of an objective function for the optimization problem. The first approach involves minimizing the transmitted power for a given quality of user service and radar surveillance. The second approach involves optimizing the quality of service for the worst radar and communication channel under a given power budget. The value that determines the quality of service is the signal-to-noise ratio, for both communication and radar.Aim. Тo solve the optimization problem of spatial linear coding of signals in a joint multicast radar and communication system, which shares a common signal.Materials and methods. Optimization of spatial linear coding in a joint radio radar and communication system was carried out by the methods of statistical theory and optimization theory using the numerical solution of optimization problems. The performance characteristics of the system were analyzed by Monte Carlo simulation. Statistical simulation was performed in the MATLAB environment using standard tools, as well as the CVX package for the numerical solution of convex optimization problems.Results. Optimization problems were formulated based on the criteria of the minimum radiated power and the maximum signal-to-noise ratio in the worst channel. A limitation on the radiated power of individual antenna channels was used for both cases. Optimization problems were approximately reduced to convex problems with semidefinite constraints, which could be solved using the wellknown interior point algorithm with polynomial complexity. The performed statistical simulation produced optimal performance characteristics of a joint system, including the total power versus the threshold signal-to-noise ratio and the signal-to-noise ratio for the worst channel versus the power budget.Conclusion. The proposed numerical optimization methods for spatial linear coding in a transmitting antenna array can be recommended when designing joint radar communication systems.

Spectral Efficiency of Wireless Relay Network in Frequency Non-Selective Channel

Introduction. A wireless communication system based on a relay network where a link between a source and a destination is carried out through a network of relay nodes have been considered. Relay networks operate according with amplifier-and-forward protocol where each relay node performs reception, amplifying, phase shifting and retranslation of a signal to the destination node. As a result a task of powers and phases optimization in the relay nodes (i.e. the complex weighted coefficients optimization) becomes actual. Complex weighted coefficients of the relay nodes are optimized in such a way as to ensure the maximum signal to noise ratio at the receiver while limiting a power emitted by the relay nodes. In the paper, optimization of spatial processing with different a priori channel state information (i.e. instantaneous channel state information and the second order statistics) have been considered. Aim. Spectral efficiency analysis of a relay network in a multipath channel where the relay network was optimized by using of two types a priori information: an instantaneous channel state information and second order statistics. Materials and methods. Optimization of spatial signal processing in the relay network was based on methods of statistical theory and optimization using analytics of linear algebra and methods of mathematical programming. Performances of the relay network were analyzed using Monte Carlo simulation. The simulation was performed in MATLAB program environment using CVX toolbox for solving convex optimization task. Results. In the paper optimal solutions for spatial signal processing in the relay network were presented. The solutions were based on maximum of signal to noise ratio while limiting total relay power and individual power of relay nodes. Monte Carlo simulation was performed to provide performances of the relay network for different types of channel state information and channel parameters. Mean capacities versus mean source power, a budget of relay nodes power and a ratio between random and deterministic power of the channel were gained for the Rayleigh model of multipath channel. Conclusions. The results have a practical application. Thus, the use of the second order statistics is possible in relay networks when direct visibility with a low level of background from local objects is provided. In urban areas, where shading and multipath propagation of signals occur, it is possible to use only an approach based on the knowledge of channel instantaneous state.

Statistical Methods in Theory of Technical Systems

Today’s society is served by modern technology, accompanied by effects of insecurity and uncertainty, which are important and inevitable. Engineering analysis must include methods of assessing these impacts on the design, implementation and operation of technical systems. Mathematical statistics and probability theory provide the mathematical basis for modeling unreliability and analysis as well as their impact on already built technical systems. The aim of the paper is to introduce quantitative methods that enable systematic development of planned and constructed criteria, problem modeling and evaluation of economically technical optimum.

Surface for methane combustion: O(3P) +CH4 → OH+CH3**Project supported by the National Natural Science Foundation of China (Grant No. 51574016) and completed while the author was in residence at UNSW, Australia supported by the International Cooperation Training Program for Innovative Talents of USTB.

Kinetic investigations including quasi-classical trajectory and canonical unified statistical theory method calculations are carried out on a potential energy surface for the hydrogen-abstraction reaction from methane by atom O(3P). The surface is constructed using a modified Shepard interpolation method. The ab initio calculations are performed at the CCSD(T) level. Taking account of the contribution of inner core electrons to electronic correlation interaction in ab initio electronic structure calculations, modified optimized aug-cc-pCVQZ basis sets are applied to the all-electrons calculations. On this potential energy surface, the triplet oxygen atom attacks methane in a near-collinear H–CH3 direction to form a saddle point with barrier height of 13.55 kcal/mol, which plays a key role in the kinetics of the title reaction. For the temperature range of 298–2500 K, our calculated thermal rate constants for the O(3P) + CH4 → OH + CH3 reaction show good agreement with relevant experimental data. This work provides detailed mechanism of this gas-phase reaction and a theoretical guidance for methane combustion.

Wavelet regression estimations for negatively associated sample

ABSTRACT This paper considers wavelet estimations for a regression function based on negatively associated data. We provide upper bounds of mean integrated squared error of wavelet estimators in Besov space. It turns out that our theorem reduces to the theorem of Chesneau and Shirazi [Nonparametric wavelet regression based on biased data. Comm Statist Theory Methods. 2014;43:2642–2658], when the random sample is independent.

Exploring the methane combustion reaction: A theoretical contribution**Project supported by the National Natural Science Foundation of China (Grant Nos. 51574016 and 51604018).

This paper represents an attempt to extend the mechanisms of reactions and kinetics of a methane combustion reaction. Three saddle points (SPs) are identified in the reaction using the complete active space self-consistent field and the multireference configuration interaction methods with a proper active space. Our calculations give a fairly accurate description of the regions around the twin first-order SPs (3A′ and 3A″) along the direction of O(3P) attacking a near-collinear H–CH3. One second-order SP2nd (3E) between the above twin SPs is the result of the C3v symmetry Jahn–Teller coupling within the branching space. Further kinetic calculations are performed with the canonical unified statistical theory method with the temperature ranging from 298 K to 1000 K. The rate constants are also reported. The present work reveals the reaction mechanism of hydrogen-abstraction by the O(3P) from methane, and develops a better understanding for the role of SPs. In addition, a comparison of the reactions of O(3P) with methane through different channels allows a molecule-level discussion of the reactivity and mechanism of the title reaction.

Estimation and diagnostic analysis in skew-generalized-normal regression models

ABSTRACTThe skew-generalized-normal distribution [Arellano-Valle, RB, Gómez, HW, Quintana, FA. A new class of skew-normal distributions. Comm Statist Theory Methods 2004;33(7):1465–1480] is a class of asymmetric normal distributions, which contains the normal and skew-normal distributions as special cases. The main virtues of this distribution is that it is easy to simulate from and it also supplies a genuine expectation–maximization (EM) algorithm for maximum likelihood estimation. In this paper, we extend the EM algorithm for linear regression models assuming skew-generalized-normal random errors and we develop a diagnostics analyses via local influence and generalized leverage, following Zhu and Lee's approach. This is because Cook's well-known approach would be more complicated to use to obtain measures of local influence. Finally, results obtained for a real data set are reported, illustrating the usefulness of the proposed method.

ОЦЕНКА ДОСТОВЕРНОСТИ ПРЕОБРАЗОВАНИЯ ИНФОРМАЦИИ В ИНФОРМАЦИОННЫХ СИСТЕМАХ

Objective: To find the method of data processing validation in the process of data systems engineering (IS), that provides for reliability of information at different stages of data processing (keying, reading different types of transfer support, storing, channeling, processing, presenting results to the user, etc.). Methods: The methods of statistical theory of reliability and the theory of information coding were applied, as the reliability of control options (by a human-operator, by means of hardware device, via program, etc.) significantly differs which leads to efficiency changes of one and the same method, depending on its concrete implementation. Measures on reducing a number of occurring distortions were taken in addition to error control methods. Commonly used parameters of the given methods prevent from the unified position assessment of the simultaneous application effect of different control methods and measures, aimed at reducing the number of errors, not related to control, taking into account their mutual influence, reliability and implementation structure. Results: The task of using different methods of error control (protective coding, checking sums application, duplication of operations with results comparison, data visual inspection, acceptable range check when entering some data, etc.) was solved, as well as the methods not related to control (the selection of input values from a pre-arranged list, errorfree performance of the staff incentive, etc.). In the process of IS engineering it became possible to assess the effect from application of a separate method and a group of different methods of reliability improvement at different stages of data processing. Practical importance: The considered approach makes it possible to assess detectivity of separate and the complex of control methods at the stages of data conversion in the process of IS engineering, as well as to consider from unified positions the impact of measures, not related to control, on information integrity.

Estimation of the limit variance for sums under a new weak dependence condition

ABSTRACTWe prove a self-normalized central limit theorem for a mixing class of processes introduced in Kacem M, Loisel S, Maume-Deschamps V. [Some mixing properties of conditionally independent processes. Commun Statist Theory Methods. 2016;45:1241–1259]. This class is larger than more classical strongly mixing processes and thus our result is more general than [Peligrad M, Shao QM. Estimation of the variance of partial sums for ρ-mixing random variables. J Multivar Anal. 1995;52:140–157; Shi S. Estimation of the variance for strongly mixing sequences. Appl Math J Chinese Univ. 2000;15(1):45–54] ones. The fact that some conditionally independent processes satisfy this kind of mixing properties motivated our study. We investigate the weak consistency as well as the asymptotic normality of the estimator of the variance that we propose.

Mechanism and Kinetics of Methane Combustion, Part I: Thermal Rate Constants for Hydrogen-Abstraction Reaction of CH4 + O(3P).

The mechanism and kinetics of gas-phase hydrogen-abstraction by the O(3P) from methane are investigated using ab initio calculations and dynamical methods. Not only are the electronic structure properties including the optimized geometries, relative energies, and vibrational frequencies of all the stationary points obtained from state-averaged complete active space self-consistent field calculations, but also the single-point energies for all points on the intrinsic reaction coordinate are evaluated using the internally contracted multireference configuration interaction approach with modified optimized cc-pCVDZ basis sets. Our calculations give a fairly accurate description of the regions around the 3A″ transition state in the O(3P) attacking a near-collinear H-CH3 direction with a barrier height of 12.53 kcal/mol, which is lower than those reported before. Subsequently, thermal rate constants for this hydrogen-abstraction are calculated using the canonical unified statistical theory method with the temperature ranging from 298 K to 1000 K. These calculated rate constants are in agreement with experiments. The present work reveals the reaction mechanism of hydrogen-abstraction by the O(3P) from methane, and it is helpful for the understanding of methane combustion.

The Almon two parameter estimator for the distributed lag models

ABSTRACTThe two parameter estimator proposed by Özkale and Kaçıranlar [The restricted and unrestricted two parameter estimators. Comm Statist Theory Methods. 2007;36(15):2707–2725] is a general estimator which includes the ordinary least squares, the ridge and the Liu estimators as special cases. In the present paper we introduce Almon two parameter estimator based on the two parameter estimation procedure to deal with the problem of multicollinearity for the distiributed lag models. This estimator outperforms the Almon estimator according to the matrix mean square error criterion. Moreover, a numerical example and a Monte Carlo simulation experiment are presented by using different estimators of the biasing parameters.

Exact likelihood inference for two exponential populations based on a joint generalized Type-I hybrid censored sample

Following the work of Chen and Bhattacharyya [Exact confidence bounds for an exponential parameter under hybrid censoring. Comm Statist Theory Methods. 1988;17:1857–1870], several results have been developed regarding the exact likelihood inference of exponential parameters based on different forms of censored samples. In this paper, the conditional maximum likelihood estimators (MLEs) of two exponential mean parameters are derived under joint generalized Type-I hybrid censoring on the two samples. The moment generating functions (MGFs) and the exact densities of the conditional MLEs are obtained, using which exact confidence intervals are then developed for the model parameters. We also derive the means, variances, and mean squared errors of these estimates. An efficient computational method is developed based on the joint MGF. Finally, an example is presented to illustrate the methods of inference developed here.

Interplay between detection strategies and stochastic resonance properties

We discuss how to exploit stochastic resonance with the methods of statistical theory of decisions. To do so, we evaluate two detection strategies: escape time analysis and strobing. For a standard quartic bistable system with a periodic drive and disturbed by noise, we show that the detection strategies and the physics of the double well are connected, inasmuch as one (the strobing strategy) is based on synchronization, while the other (escape time analysis) is determined by the possibility to accumulate energy in the oscillations. The analysis of the escape times best performs at the frequency of the geometric resonance, while strobing shows a peak of the performances at a special noise level predicted by the stochastic resonance theory. We surmise that the detection properties of the quartic potential are generic for overdamped and underdamped systems, in that the physical nature of resonance decides the competition (in terms of performances) between different detection strategies.

Random number generation and estimation with the bimodal asymmetric power-normal distribution

Recently, Bolfarine et al. [Bimodal symmetric-asymmetric power-normal families. Commun Statist Theory Methods. Forthcoming. doi:10.1080/03610926.2013.765475] introduced a bimodal asymmetric model having the normal and skew normal as special cases. Here, we prove a stochastic representation for their bimodal asymmetric model and use it to generate random numbers from that model. It is shown how the resulting algorithm can be seen as an improvement over the rejection method. We also discuss practical and numerical aspects regarding the estimation of the model parameters by maximum likelihood under simple random sampling. We show that a unique stationary point of the likelihood equations exists except when all observations have the same sign. However, the location-scale extension of the model usually presents two or more roots and this fact is illustrated here. The standard maximization routines available in the R system (Broyden–Fletcher–Goldfarb–Shanno (BFGS), Trust, Nelder–Mead) were considered in our implementations but exhibited similar performance. We show the usefulness of inspecting profile loglikelihoods as a method to obtain starting values for maximization and illustrate data analysis with the location-scale model in the presence of multiple roots. A simple Bayesian model is discussed in the context of a data set which presents a flat likelihood in the direction of the skewness parameter.

Local random structure of supercritical carbon dioxide

Data on coherent anti-Stokes Raman scattering (CARS) spectroscopy of supercritical CO2 are analyzed by methods of statistical theory. The following is shown. The random local structure of supercritical CO2 is laminated at the critical density and a temperature of 33°C. The layer thickness is no more than 8 nm. The average layer density exceeds the critical density by 1%. The fraction of local layers rarefied by density fluctuations exceeds the fraction of layers compacted by fluctuations by 8%. The characteristic quantity of the local fluctuation of the density is 8% of the critical value of the density. The lifetime of local fluctuations of the density is ∼10−10 s.

Probability and structural reliability assessment of mortar joint thickness in load-bearing masonry walls

Mortar joint thickness has a significant effect on capacity of structural masonry. Data on mortar joint thickness (bed and head joints) were collected from twelve typical storey-high walls at three different building sites and from four walls built in a research laboratory in Switzerland. The data obtained allowed an analysis of the spatial distribution of the joint thickness in each wall and the characterization of the probability distribution of joint thickness. The data has been statistically analysed and the results discussed: the central and dispersion measures were calculated and several probability distributions have been fitted to the sample data and subsequently tested using standard methods of statistical theory. Further, the results obtained from all four building sites have been compared, thus providing quantitative information about the quality of the work on different sites. The presented probabilistic information is then used to define reliability-based limit state specifications where the joint thickness acts as an important random variable. The reliability of the structural masonry subjected to a concentric normal force found that probabilistic modelling of bed joint thickness results in higher reliability indices.

Multivariate Analysis of Variance Applied to 3G Mobile Market Segmentation : The Innovator Theory

Mobile communication and Internet are the most thriving industries in the 21st century. They tend to integrate recently. Human beings are used to construct a beautiful dream in communication: An internet service which can be enjoyed by a mobile and dexterous device. This article explores the demand of 3G cell phone consumers in Taiwan from the angle of technical management. Here we use the method of statistical theory and electrical machinery communication background to explain it. We also make the further market classification for the consumer. The findings have clas sified three clusters, VIP gold customer group possesses 34% most races grouping in earlier period which emphasized for the technical management. This cluster has a quantity demand to network, also is highly relative in each kind of function demands. We should pay attention to the degree of satisfaction from the consumer of this cluster. The population variable in this cluster, which the proportion is high in the transaction officer and the housekeeper, the age between 18� 34 year-old, the scholarship is college, the incomes each month is above NT$50,000, the female possess the most proportion, therefore, by higher proportion to these variables, we cou ld propose the special marketing project and the cell phones with the corresponding functions. By taking the chance, we can construct the 3G communication tyrant industry.