Statistical Distribution Of Data Research Articles

Data-Distribution-Aware Fuzzy Rough Set Model and its Application to Robust Classification.

Fuzzy rough sets (FRSs) are considered to be a powerful model for analyzing uncertainty in data. This model encapsulates two types of uncertainty: 1) fuzziness coming from the vagueness in human concept formation and 2) roughness rooted in the granulation coming with human cognition. The rough set theory has been widely applied to feature selection, attribute reduction, and classification. However, it is reported that the classical FRS model is sensitive to noisy information. To address this problem, several robust models have been developed in recent years. Nevertheless, these models do not consider a statistical distribution of data, which is an important type of uncertainty. Data distribution serves as crucial information for designing an optimal classification or regression model. Thus, we propose a data-distribution-aware FRS model that considers distribution information and incorporates it in computing lower and upper fuzzy approximations. The proposed model considers not only the similarity between samples, but also the probability density of classes. In order to demonstrate the effectiveness of the proposed model, we design a new sample evaluation index for prototype-based classification based on the model, and a prototype selection algorithm is developed using this index. Furthermore, a robust classification algorithm is constructed with prototype covering and nearest neighbor classification. Experimental results confirm the robustness and effectiveness of the proposed model.

Data distributions in magnetic resonance images: A review

Many image processing methods applied to magnetic resonance (MR) images directly or indirectly rely on prior knowledge of the statistical data distribution that characterizes the MR data. Also, data distributions are key in many parameter estimation problems and strongly relate to the accuracy and precision with which parameters can be estimated. This review paper provides an overview of the various distributions that occur when dealing with MR data, considering both single-coil and multiple-coil acquisition systems. The paper also summarizes how knowledge of the MR data distributions can be used to construct optimal parameter estimators and answers the question as to what precision may be achieved ultimately from a particular MR image.

The investigation of the difference between accounting data error in future operational cash flow predication, before and after adjust, due to inflation in accepted companies in Tehran stock exchange

The present research examines the difference between accounting data error in future operational cash flow predication before and after adjust due to inflation the population in this research include the accepted companies in Tehran stock exchange. The sample member companies financial statements by mean of current value – constant Rials were adjusted and were accounting data error in future and before adjust due to accounting inflation. After examination of the accounting data prediction before and after adjust, statistical data were tested by means of jariko method so that their normality by examined. The obtained results of jariko-Bera test indicate that the statistical data distribution is not normal. Therefore the sample couple signal Nonparametic test is used for investigation of difference between accounting data error in future cash floe prediction before and after adjust. the research hypothesis is : The accounting data error based on historical values is move than accounting data error based on current values in future period operational cash flow. The obtained results of sample even signal in relation to research hypothesis indication that we can accept the research hypothesis Normal 0 false false false EN-US X-NONE AR-SA

Natural background level assessment in groundwaters: probability plot versus pre-selection method

The need for a sound methodology to establish a formal value separating natural geochemical background levels in groundwaters from the anthropogenic impact, is perceived especially from a legal point of view. In this research we compare the natural background levels derived for As, F, Mn and Fe in a volcanic-sedimentary aquifer in Central Italy, using probability plots and pre-selection methods. The derived values may differ by even two orders of magnitude for strongly skewed distributions. Results show that both methods have a degree of subjectivity, however the integration of the two methods reinforces the validity of the assessment. Critical issues include statistical data distribution choice, minimum population size, distance of the sampling sites from anthropized areas. Pre-selection methods appear more robust than probability plots when the hydrogeological asset is duly considered. The greater importance of the aquifer conceptual model of the system, than the choice of a statistical method, is pointed out.

A Modified Simulation-Based Multi-Signal Modeling for Electronic System

Multi-signal model is an effective modeling method applicable to large scale complex system. In this paper, an improved simulation-based modeling method for parametric fault is put forward. Two times of Monte-Carlo simulation are done in normal tolerance. Based on the estimated sample variance obtained from the first Monte-Carlo simulation, the analysis runs of the second Monte-Carlo is determined empirically to reduce the simulation cost. Then the statistical distribution of data from the second Monte-Carlo simulation is judged qualitatively by normality test. After that, an adaptive method is adopted to estimate the threshold range for signal feature in normal state, which can improve modeling precision. At last, the effectiveness of the proposed method is verified and the performances are compared to manifest the advantage of the proposed method. The work in this paper is valuable for future further research of complex system test and diagnosis based on multi-signal.

Correlations in between EAWS and OCRA Index concerning the repetitive loads of the upper limbs in automobile manufacturing industries

Upper limbs repetitive tasks are one of the main sources of risk for the workers of the manufacturing industries and the standards ISO 11228-3 and EN 1005-5 addressed this issue since 2007. EAWS (European Assembly Worksheet) is a 1st level ergonomic risk assessment method and it provides in its 4th section a score to measure the load level for the upper limbs based on a traffic light scheme. According to the relevant ISO/CEN standards, the OCRA Index is the preferred system to refer to in the evaluation of the biomechanical stress of hand-harm-shoulder system. This correlation study is based on a 45 workstations sample coming from the automobile manufacturing industry. According to the results, EAWS4 shows an excellent correlation with OCRA index (Spearman's rho correlation index 0.95). Being EAWS based on biometric statistical data distribution, its typical application is the process design phase, but adopting a conservative approach in the interpretation of EAWS4 score for risk mapping purposes, it provides an equivalent "reaction" pattern (countermeasures to be taken in the production phase) with respect of OCRA Index with an Odds Ratio ranging from 0.89 (OR-matched) to 1.00 (OR-conservative).

Comparison of Combinatorial Clustering Methods on Pharmacological Data Sets Represented by Machine Learning-Selected Real Molecular Descriptors

Cluster algorithms play an important role in diversity related tasks of modern chemoinformatics, with the widest applications being in pharmaceutical industry drug discovery programs. The performance of these grouping strategies depends on various factors such as molecular representation, mathematical method, algorithmical technique, and statistical distribution of data. For this reason, introduction and comparison of new methods are necessary in order to find the model that best fits the problem at hand. Earlier comparative studies report on Ward's algorithm using fingerprints for molecular description as generally superior in this field. However, problems still remain, i.e., other types of numerical descriptions have been little exploited, current descriptors selection strategy is trial and error-driven, and no previous comparative studies considering a broader domain of the combinatorial methods in grouping chemoinformatic data sets have been conducted. In this work, a comparison between combinatorial methods is performed,with five of them being novel in cheminformatics. The experiments are carried out using eight data sets that are well established and validated in the medical chemistry literature. Each drug data set was represented by real molecular descriptors selected by machine learning techniques, which are consistent with the neighborhood principle. Statistical analysis of the results demonstrates that pharmacological activities of the eight data sets can be modeled with a few of families with 2D and 3D molecular descriptors, avoiding classification problems associated with the presence of nonrelevant features. Three out of five of the proposed cluster algorithms show superior performance over most classical algorithms and are similar (or slightly superior in the most optimistic sense) to Ward's algorithm. The usefulness of these algorithms is also assessed in a comparative experiment to potent QSAR and machine learning classifiers, where they perform similarly in some cases.

On the smoothing of multinomial estimates using Liouville mixture models and applications

There has been major progress in recent years in statistical model-based pattern recognition, data mining and knowledge discovery. In particular, generative models are widely used and are very reliable in terms of overall performance. Success of these models hinges on their ability to construct a representation which captures the underlying statistical distribution of data. In this article, we focus on count data modeling. Indeed, this kind of data is naturally generated in many contexts and in different application domains. Usually, models based on the multinomial assumption are used in this case that may have several shortcomings, especially in the case of high-dimensional sparse data. We propose then a principled approach to smooth multinomials using a mixture of Beta-Liouville distributions which is learned to reflect and model prior beliefs about multinomial parameters, via both theoretical interpretations and experimental validations, we argue that the proposed smoothing model is general and flexible enough to allow accurate representation of count data.

The estimation of absorbed dose rates for non-human biota: an extended intercomparison

An exercise to compare 10 approaches for the calculation of unweighted whole-body absorbed dose rates was conducted for 74 radionuclides and five of the ICRP's Reference Animals and Plants, or RAPs (duck, frog, flatfish egg, rat and elongated earthworm), selected for this exercise to cover a range of body sizes, dimensions and exposure scenarios. Results were analysed using a non-parametric method requiring no specific hypotheses about the statistical distribution of data. The obtained unweighted absorbed dose rates for internal exposure compare well between the different approaches, with 70% of the results falling within a range of variation of±20%. The variation is greater for external exposure, although 90% of the estimates are within an order of magnitude of one another. There are some discernible patterns where specific models over- or under-predicted. These are explained based on the methodological differences including number of daughter products included in the calculation of dose rate for a parent nuclide; source-target geometry; databases for discrete energy and yield of radionuclides; rounding errors in integration algorithms; and intrinsic differences in calculation methods. For certain radionuclides, these factors combine to generate systematic variations between approaches. Overall, the technique chosen to interpret the data enabled methodological differences in dosimetry calculations to be quantified and compared, allowing the identification of common issues between different approaches and providing greater assurance on the fundamental dose conversion coefficient approaches used in available models for assessing radiological effects to biota.

Extreme value statistics for river quality simulations

Various methods have been proposed to assess intermittent pollution loads and impacts on rivers in urban areas. Although the variables to describe the impact are mainly the same, the standards show significant differences in the assessment of permitted concentration level, duration and return period. The probability of an event is derived using either frequencies of occurrence or predefined extreme value distributions. Both methods have drawbacks. To bypass these, an a posteriori estimation of the statistical distribution of data based on the peak-over-threshold method is proposed. The method is exemplarily demonstrated using a semi-virtual case study.

New Calibration Methodology for Microscopic Traffic Simulation Using Enhanced Simultaneous Perturbation Stochastic Approximation Approach

Traffic simulation models can represent real-world conditions such as delays, travel times, queues, and flows. However, accurate evaluation of these traffic conditions depends on the selection of model parameters and the calibration methodology. Most previous calibration studies have focused on minimizing the sum of the differences between the observed data and simulation output during a certain time period on a typical day. However, to capture a realistic distribution of all possible traffic conditions, a more general calibration methodology that can be used with any traffic condition is required. This paper proposes a new calibration methodology–-the Bayesian sampling approach in conjunction with the application of the simultaneous perturbation stochastic approximation (SPSA) optimization method [enhanced SPSA (E-SPSA)]–-that enables the modeler to enhance calibration by considering statistical data distribution. Instead of calibrating with input data for certain time periods, calibration is performed with data obtained from a complete input distribution. Mean square variation (MSV) was used to evaluate the accuracy of the proposed E-SPSA calibration approach. On the basis of the MSV of flows, the MSV value of the E-SPSA methodology was found to be 0.940, which was greater than the variation of speed obtained from SPSA-only (0.897) or from a variation approach (0.888). Thus, this proposed methodology not only makes it possible to overcome some of the limitations of previous calibration approaches, but also improves the results of simulation model calibration by accurately capturing a wide range of real-world conditions. Future work will focus on testing the proposed calibration methodology using more extensive data sets and models developed using simulation tools other than PARAMICS.

On the Consistency of the Normalized Eight-Point Algorithm

A recently proposed argument to explain the improved performance of the eight-point algorithm that results from using normalized data (Chojnacki, W., et al. in IEEE Trans. Pattern Anal. Mach. Intell. 25(9):1172---1177, 2003) relies upon adoption of a certain model for statistical data distribution. Under this model, the cost function that underlies the algorithm operating on the normalized data is statistically more advantageous than the cost function that underpins the algorithm using unnormalized data. Here we extend this explanation by introducing a more refined, structured model for data distribution. Under the extended model, the normalized eight-point algorithm turns out to be approximately consistent in a statistical sense. The proposed extension provides a link between the existing statistical rationalization of the normalized eight-point algorithm and the approach of Muhlich and Mester for enhancing total least squares estimation methods via equilibration. The paper forms part of a wider effort to rationalize and interrelate foundational methods in vision parameter estimation.

A Preliminary Assessment Of BTX Pollution InUrban Air In The City Of Lanzhou

A multi-pollutant assessment of Benzene, Toluene and Xylene was performed in the Chinese urban environment of Lanzhou city by means of diffusive samplers. The focus was upon an assessment of the interrelationships between different pollutants and different types of sampling sites. The considerable number of samples taken with the technique proposed in this work allows for the statistical treatment of data along the space coordinates. That is very useful in air quality management and control, due to the possibility to infer the statistical distribution of data and compare its parameters with reference values, such as mean, limit or standard values, etc. It was found that distributions of BTX are successfully estimated from a statistical point of view from the Normal distribution. Therefore, it was demonstrated that the passive sampling method can be used in a large-scale project for the measurements of BTX spatial variability at extremely low cost. Errors found in measurement technique are extremely small and valuable for the purposes of this work. Moreover, many of the measurement sites in this study could not be operated using conventional methods due to the difficulties in transportation, power supply, location, etc. Thus this technique allows to map big areas difficult to be reached with heavy or large instrumentation.

Ogive-based Legends for Choropleth Mapping

Exploratory data analysis and geovisualization have opened new paths for displaying and analyzing data. Alternate views of the same data set provide more insight into the nature of the data. The choropleth map has been the primary display device for portraying the spatial distribution of statistical data aggregated over areal units. However, the standard choropleth map is not as informative with respect to the statistical distribution of the data. Data classification for classed choropleth maps, as well as the transformation of numeric values into lightness values, filters out much of the information regarding the underlying statistical distribution of the data. Traditionally, the map legend has the role of connecting lightness values to their numeric counterparts and providing some information regarding the statistical properties of the data. It is proposed here that a more versatile legend can be constructed based on the ogive cumulative frequency diagram. Ogive legends can present the overall statistical distribution of data in its natural state without resorting to data aggregation, as do histograms and other frequency diagrams. Furthermore, ogive legends can display the distribution of data within any individual class interval.

Non-linearity in radiocaesium soil to plant transfer: Fact or fiction?

The basis premise of many radiological assessments is the assumption that the transfer of many radionuclides from soil to herbage and hence animal derived food products is a positive linear relationship for a given set of ecological conditions. However, a number of authors have published results, which they conclude demonstrate non-linear transfer of radiocaesium to plants and animals with transfer being highest when soil concentrations are lowest. Whilst we may expect non-linear transfer of radionuclides under homeostatic control or present in comparatively large chemical quantities, there appears no credible hypothesis to support such an observation for radiocaesium. In this paper we review those articles, which have reported non-linear radiocaesium transfer and also analyse novel data. We argue that saturation of Cs uptake as suggested by some other authors is unlikely. Sampling bias, statistical data distribution and countermeasure application are suggested as potential contributors. However, we have not been able to provide a conclusive reason for such observations. Given the important implications for foodchain modelling further consideration of available data is required to more comprehensively answer this question.

Machine vision-based gray relational theory applied to IC marking inspection

In the semiconductor industry, IC marking error remains a problem. The objective of this study is to identify IC marking using gray relational analysis. The gray theorem determines the gray relational grades of all of the selected factors by choosing the highest gray relational grade, even under incomplete information circumstances. In an IC marking identification procedure, an image is rotated and segmented first. Second, thresholding and thinning operations are applied to reduce the calculation complexity and extract features from the segmented image. Finally, the gray relational analysis method is applied to inspect the IC markings. The identification rate reaches 97.5%. As compared to traditional methods, there are three advantages in gray relational analysis: 1) No large amount of data is needed; 2) No specific statistical data distribution is required; and 3) There is no requirement for the independency of the factors to be considered. It is an easy and practical method in the field of IC marking inspection.

<sup>137</sup>Cs and <sup>134</sup>Cs Human Internal Contamination in Italy Following the 1986 Chernobyl Event

A synthesis of the data concerning the distribution and behaviour over time until September 1989 of 134Cs and 137Cs human contamination deriving from the accident to Unit 4 of the Chernobyl Nuclear Power Station on 26 April 1986, is presented. The controls have been performed by means of two intercalibrated whole-body counters on healthy adult male and female volunteers living in different Italian regions. The main topics investigated are: the behaviour over time of the contamination in Bologna and Rome: geographic distribution in Italy in September 1987; the statistical distribution of data; the variability of the individual activity in relation to the mean activity of homogeneous groups; the intersex differences; and the effect of the element's biokinetics uncertainties on the committed effective dose equivalent evaluation. Trends are also found, mainly useful where extended contamination involves too large a fraction of the population for individual control of all the subjects concerned, thus requiring the identification of small groups of individuals representative of large population groups.

The properties of random trees

Consider an s-ary tree (in which every node has no more than s children). Each node holds a single datum, including a key. These are the occupied, internal, or closed nodes of the data structure. Augment the tree, following D. E. Knuth, by adding a set of unoccupied, external, open, or free nodes, so that every internal node now has just s children and every external node has no children. We assume that there is an unambiguous rule, depending only on the key values at the internal nodes of the tree, whereby a new datum, with a new key value, will be inserted at one of the external nodes; this node then becomes internal and acquires s new external nodes as children. We further assume that the rule and the statistical distribution of data are such that every external node has equal probability of being selected for insertion of a new datum, at every stage. Various statistics of such trees are now obtained explicitly, in a systematic manner which may be extended to higher moments. The principal result is that the average level of both internal and external nodes in a given tree is asymptotic in probability to [ s (s−1)]log m as m → ∞, where m is the number of internal nodes in the tree. Since the corresponding average level for a k-level fully balanced tree [with m = (s k−1) (s−1) ] is asymptotic to k ≈ log s m = ( l log s )log m as m → ∞, we conclude that, unless the distribution of data is far from the rather plausible assumption made here, it is highly improbable that the considerable cost of rebalancing trees when constructing data-bases will ever be justified in practice.

Exposure to agricultural treatment residues: Some simple statistical considerations based on monitoring data for ethoxyquin on apples

The data examined here concern ethoxyquin levels, mainly measured in apple samples from the retail market. In this study about three hundred measurements, carried out on apples in Northern-Central Italy and recently published, are examined, with the purpose of defining the main characteristics of value statistical distribution and variability and to optimize sampling criteria. The analysis did not indicate the presence of significantly high levels or consequently significantly high risks; nevertheless, it pointed out some important aspects in data collection and evaluation. First, it appeared that the statistical distribution of data is typically nonsymmetrical, non-Gaussian, and characterized by a tail extending toward the high values. The logarithmic transformation of data appeared useful in order to obtain a Gaussian distribution. As a rule, the data variability appeared to be high. The frequency and distribution of values above the analytical threshold resulted in significant change, both in time and in space. The percentage of positive values (above the analytical threshold) appeared to vary up to a factor of 2–3, as analogously did their geometric mean. The analysis of statistical distributions of such values indicated that (i) the geometric mean of data may be considered the best indicator of their central tendency; (ii) the standard deviation of measurement carried out in the same place and in the same year may range from 0.7 to 1 for log-transformed data, which means approximately a factor of 2–3 for original data (two standard deviations correspond to a factor of 4–9); (iii) 95% of the residue level population, under conditions similar to those examined here, may be reasonably expected to fall within a value 5- to 15-fold higher than the geometric mean of data (with a 95% confidence level); (iv) this last aspect is due to lognormal distribution features which imply the possible presence of a slight number of high values together with a large number of much lower values. This preliminary study indicates that a risk of possible sporadic significant exposure levels may exist; it is, however, very important to identify whether highest exposure levels are randomly distributed in space and time or rather affect a specific group of subjects in a specific period.

An analysis of the accuracy of time-of-flight ranging at very low signal levels

A study is made of the statistical distribution of data in pulsed laser ranging arising from random fluctuations in the return signal and the accumulation of jitter in the timing measurements. Signal detection by leading edge discrimination and pulse reconstruction techniques is considered in single-shot and multi-shot applications. Consideration is given to the possibility of using different methods of data analysis to reduce the final error in multi-shot experiments.