Probability Distribution Of Values Research Articles

Regional sub-hourly extreme rainfall estimates in Sicily under a scale invariance framework

Design of urban drainage systems or flood risk assessment in small catchments often requires knowledge of very short-duration rainfall events (less than 1 h). Unfortunately, data for these events are often unavailable or too scarce for a reliable statistical inference. However, regularities in the temporal pattern exhibited by storm records, known as scaling properties of rainfall, could help in characterizing extreme storms at partially gauged sites better than the application of traditional statistical techniques. In this work, a scaling approach for estimating the distribution of sub-hourly extreme rainfall in Sicily (Italy) is presented based on data from high-resolution rain gauges with a short functioning period and from low-resolution rain gauges with longer samples. First, simple scaling assumption was tested for annual maxima rainfall (AMR) data from 10 min to 24 h duration, revealing that the simple scaling regime holds from 20 to 60 min for most of the stations. Then, scaling homogeneous regions were classified based on the values of the scaling exponent. In each region, this parameter was regionalized through power-law relationships with the median of 1 h AMR data. After that, regional Depth Duration Frequency (DDF) curves were developed by combining the scale-invariant framework with the generalized extreme value (GEV) probability distribution and used to estimate T-year sub-hourly extreme rainfalls at sites where only rainfall data for longer durations (≥ 1 h) were available. The regional GEV simple scaling model was validated against sub-hourly historical observations at ten rain gauges, generally yielding, in relation to the scaling exponent value, to similar or better sub-hourly estimates than empirical approach.

A novel, Value-Focused-Thinking based, approach for modelling agro-industrial decisions under scarce information

Agro-industrial decision-making is hampered by several, variously-natured, uncertainties. As uncertainty reduction is expensive, the decision modelling process for these industries must strive to use all available information. However, said inclusive effort should be accompanied by an effort to keep modelling assumptions transparent. This work shows the development, from a Value-Focused Thinking perspective, of a model to assess alternatives for improving the operation of a cattle fodder producer. Modelling starts by analyzing and structuring the owner’s objectives and proceeds by systematically characterizing, via value judgments or probability distributions, the connections between structured objectives. Constructing the model over a blueprint of connected objectives allows a faithful representation of the understanding of the system behavior while the methodical, one-connection-at-a-time, modelling procedure renders the assumptions used to operationalize each connection visible, facilitating their replacement if more information becomes available. The modelling approach put forward here can support industrial decision making with limited information.

An evaluation of a multi-day rainfall – runoff volume – peak discharge transform for flood frequency estimation

ABSTRACT A new method to estimate design discharge quantiles is described based on converting multi-day rainfall P to flood event runoff RO, factored to generate discharge Q. The so-called PROQ transfer function is founded on simple flood volume-peak and GRADEX rainfall-runoff tanh relationships. Performance testing of PROQ, in both at-site and regional design flood contexts up to 1 in 100 annual exceedance probability, was made using south east Queensland streamgauge data. A statistical comparison against proven methods showed that the PROQ transform has significant potential as an alternative for design flood estimation. An example of how PROQ can be used within a design flood framework and recommendations for further enhancement are provided. Abbreviations: AEP: Annual exceedance probability; AMS: Annual maximum series, extracted from the flood record at a gauge site; ANOVA: Analysis of variance; ARR: Australian Rainfall and Runoff guidelines; A-S: At-site. Describes a set of methods to estimate design flood quantiles by statistical analysis of the flood record at an individual gauge site; E: Nash–Sutcliffe efficiency; FFA: Flood frequency analysis; G-B: Multiple Grubbs-Beck test recommended by ARR 2019 for low flow censoring. Used for at-site flood frequency analysis; GEV: General extreme value probability distribution; GRADEX: Gradient of extreme values. Design flood probability concept originating in France based on parallelism of rainfall and runoff quantile curves; L: Retention of rainfall within the catchment during flood event, expressed as a depth; LP3: Log Pearson 3 probability distribution; P: Rainfall depth; PRM: Probabilistic Rational Method. An ARR method for ungauged, undeveloped Australian catchments superseded in 2016; PROQ: Transfer function based on converting P to RO and then factoring RO to estimate Q; PW: Palmen and Weeks. Regional method for ungauged, undeveloped Queensland catchments developed by Palmen and Weeks (2011); R: Retention curve number. Used in probabilistic charting of design floods based on PROQ; RE: Absolute relative error; REG: Regional. Describes a set of methods to estimate design flood quantiles using information obtained from at-site analyses of several representative catchments within a region; RO: Flood event runoff depth; SR30: Strike rate of estimates within ±30% tolerance.

Selection of Hydrological Probability Distributions for Extreme Rainfall Events in the Regions of Colombia

Frequency analysis of extreme events is used to estimate the maximum rainfall associated with different return periods and is used in planning hydraulic structures. When carrying out this type of analysis in engineering projects, the hydrological distributions that best fit the trend of maximum 24 h rainfall data are unknown. This study collected maximum 24 h rainfall records from 362 stations distributed throughout Colombia, with the goal of guiding hydraulic planners by suggesting the probability distributions they should use before beginning their analysis. The generalized extreme value (GEV) probability distribution, using the weighted moments method, presented the best fits of frequency analysis of maximum daily precipitation for various return periods for selected rainfall stations in Colombia.

Random matrices with prescribed eigenvalues and expectation values for random quantum states

Given a collection λ _ = { λ 1 \underline {\lambda }=\{\lambda _1 , … \dots , λ n } \lambda _n\} of real numbers, there is a canonical probability distribution on the set of real symmetric or complex Hermitian matrices with eigenvalues λ 1 , … , λ n \lambda _1, \ldots , \lambda _n . In this paper, we study various features of random matrices with this distribution. Our main results show that under mild conditions, when n n is large, linear functionals of the entries of such random matrices have approximately Gaussian joint distributions. The results take the form of upper bounds on distances between multivariate distributions, which allows us also to consider the case when the number of linear functionals grows with n n . In the context of quantum mechanics, these results can be viewed as describing the joint probability distribution of the expectation values of a family of observables on a quantum system in a random mixed state. Other applications are given to spectral distributions of submatrices, the classical invariant ensembles, and to a probabilistic counterpart of the Schur–Horn theorem, relating eigenvalues and diagonal entries of Hermitian matrices.

Finite-Size Scaling of Typicality-Based Estimates

Abstract According to the concept of typicality, an ensemble average can be accurately approximated by an expectation value with respect to a single pure state drawn at random from a high-dimensional Hilbert space. This random-vector approximation, or trace estimator, provides a powerful approach to, e.g. thermodynamic quantities for systems with large Hilbert-space sizes, which usually cannot be treated exactly, analytically or numerically. Here, we discuss the finite-size scaling of the accuracy of such trace estimators from two perspectives. First, we study the full probability distribution of random-vector expectation values and, second, the full temperature dependence of the standard deviation. With the help of numerical examples, we find pronounced Gaussian probability distributions and the expected decrease of the standard deviation with system size, at least above certain system-specific temperatures. Below and in particular for temperatures smaller than the excitation gap, simple rules are not available.

Vulnerability Mining Method for the Modbus TCP Using an Anti-Sample Fuzzer.

Vulnerability mining technology is used for protecting the security of industrial control systems and their network protocols. Traditionally, vulnerability mining methods have the shortcomings of poor vulnerability mining ability and low reception rate. In this study, a test case generation model for vulnerability mining of the Modbus TCP based on an anti-sample algorithm is proposed. Firstly, a recurrent neural network is trained to learn the semantics of the protocol data unit. The softmax function is used to express the probability distribution of data values. Next, the random variable threshold and the maximum probability are compared in the algorithm to determine whether to replace the current data value with the minimum probability data value. Finally, the Modbus application protocol (MBAP) header is completed according to the protocol specification. Experiments using the anti-sample fuzzer show that it not only improves the reception rate of test cases and the ability to exploit vulnerabilities, but also detects vulnerabilities of industrial control protocols more quickly.

Statistical modeling of annual maximum precipitation in Oued El Gourzi Watershed, Algeria

This study aims to model annual maximum precipitation based on extreme value theory for the Oued El Gourzi Watershed, Algeria. A generalized extreme value (GEV) distribution was used to determine the probability distribution of extreme values and their dependency on time for the five stations distributed across the watershed. The non-stationary models are used to represent the GEV parameters assumed an invariant shape parameter and linear functions as location and scale parameters. The best model was selected using Akaike’s information criterion and Bayesian information criterion. Stationary and non-stationary return levels for different return periods have been proposed for the study area.

Comparative Study of Statistical Analysis Methods for Nonlinear Hydrodynamic Responses of Offshore Structures

AbstractThe present study compares the statistical analysis methods for nonlinear hydrodynamic responses in offshore engineering. In particular, the Kac–Siegert and Hermite-moment methods were compared for estimating the probability distribution of the second-order responses represented via the two-term Volterra series. The Kac–Siegert method analytically formulates the probability density function (PDF) of the second-order Volterra series using an eigenvalue problem constructed with the frequency-domain transfer functions and the wave spectrum, whereas the Hermite-moment method utilizes the statistical moments to determine the coefficients of the fitting function. In addition, the probability distribution of the peak values in the second-order Volterra series with high spectral bandwidth was derived explicitly. The fatigue damage rate and the extreme response were estimated analytically. The accuracy and applicability of each method were investigated by comparing the methods with the results of the direct sampling obtained from the time series.

Combination of LS-SVM algorithm and JC method for fragility analysis of deep-water high piers subjected to near-field ground motions

The objective of this paper is to propose a novel fragility analysis method pertinent to the combination of the least squares support vector machine (LS-SVM) algorithm and JC method for the vulnerability estimation of deep-water high piers located in reservoirs under near-field ground motions. First, the uncertainties associated with the design parameters are considered and the LS-SVM algorithm is adopted to predict the cross-sectional critical curvature values of each damage state of the example pier and determine the probability distributions. Then, a group of finite element models of the example pier is developed using the OpenSees platform for considering the uncertainties related to the design parameters and near-field seismic waves; the Morrison equation is employed to calculate the added mass to simulate the hydrodynamic pressure. Meanwhile, the dynamical responses of the example pier with seven different water depth conditions are investigated using increment dynamic nonlinear analysis along the longitudinal and transverse directions under seismic excitations. Finally, the fragility functions are derived based on the JC method to consider the probability distributions of the cross-sectional critical curvature values and dynamical responses simultaneously; these functions are applied for assessing the damage probability at different damage states of the example pier. It can be concluded that the hydrodynamic pressure plays an important role in influencing the natural vibration period and mode shape of the deep-water high pier. In the slight, moderate, and extensive damage states, the damage probability of the middle-upper and bottom areas of the example pier is relatively large under longitudinal near-field seismic excitation; nevertheless, only the bottom is easily damaged under transverse near-field seismic excitation.

ОПТИМИЗАЦИЯ ПРОФИЛАКТИЧЕСКИХ ДОПУСКОВ В СЛОЖНЫХ ТЕХНИЧЕСКИХ СИСТЕМАХ

Currently, monitoring the technical condition of complex technical systems, such as electrical equipment of communication equipment, is a long and non-automated process that is carried out by operators directly at the control objects themselves. This circumstance has a negative impact on the timely detection of failures of the controlled object. One of the most difficult to detect is phasing out. For timely detection of the fact of its occurrence, it is necessary to create a control system that works in a permanent mode with pre-entered preventive tolerances. The purpose of the work is to develop a proposal for the formation of the optimal value of the preventive tolerance of the controlled parameter for detecting the fact of gradual failure and determining its probabilistic characteristics, taking into account the reservation of measurement channels. Methods used: detection of gradual failures is random and the best results are obtained using methods of statistical decision theory, the use of which assumes the presence of complete a priori information about the probability distributions of the output values of the controlled parameters. The novelty of the work is to increase the reliability and accuracy of monitoring the technical condition of complex technical objects to ensure their reliability by reserving measurement channels, which allows you to increase the accuracy of detecting gradual failure of the controlled object by optimizing the value of preventive tolerances. Result: the use of cost-effective redundancy of measurement channels, as well as the use of preventive tolerances, allows more accurate assessment of the technical condition of the control object and make a conclusion about the probability of gradual failure. Optimization of the threshold of preventive admission allows you to minimize the probability of making an erroneous decision. Practical significance: the results of the work can be used in the process of monitoring the technical condition of complex technical systems, which will avoid accidents.

FPGA-Assisted Real-Time RF Wireless Data Analytics System: Design, Implementation, and Statistical Analyses

A wide range of new ultra reliable low latency communication (URLLC) applications in next generation (NG) wireless systems demand real-time radio frequency (RF) data analytics of channel utilization (CU) that can help in making proactive resource allocation decisions. However, such real-time RF data analytics require processing of tens of millions of in-phase and quadrature (IQ) samples per second and sending huge quantities of samples to a resource allocating entity is not practical. We present design and implementation of an RF data analytics system which utilizes field-programmable gate arrays (FPGAs) at the network edge to process real-time streaming IQ samples from RF transceiver. FPGAs process millions of samples per second and output low-overhead descriptive statistics of wireless CU, such as mean CU values, maximum CU values, and entire histograms to obtain probability distribution of CU values, to a resource controller server where a quantile estimation based technique is used to detect congestion in CU in real-time. The FPGA-based modules are implemented on Xilinx's Zynq-7000 devices mounted with RF transceivers. We evaluate the performance of the implemented analytics system using extensive measurements, testing, and statistical analyses that are performed in both laboratory and over-the-air environments.

Uncertainty in Firm Valuation and a Cross-Sectional Misvaluation Measure

In valuation analysis, the degree of uncertainty associated with the value of a company is as important as the value itself. We propose an original and robust methodology for company market valuation which replaces the traditional point estimate of the conventional Discounted Cash Flow model with a probability distribution of fair values that conveys information about both the expected value of the company and its intrinsic uncertainty. Our methodology depends on two main ingredients: an econometric model for the company revenues and a set of firm-specific balance sheet relations that are estimated using historical data. We explore the effectiveness and scope of our methodology through a series of statistical exercises on publicly traded U.S. companies. At firm level, we show that the fair value distribution derived with our methodology constitutes a reliable predictor of company’s future abnormal returns. At market level, we show that a long-short valuation (LSV) factor, built using buy-sell recommendations based on the fair value distribution, contains information not accessible through traditional market factors. The LSV factor increases significantly the explanatory and predictive power of factor models estimated on portfolios and individual stocks returns.

Application of Fractal and Gray-Level Co-Occurrence Matrix Indices to Assess the Forest Dynamics in the Curvature Carpathians—Romania

The mountain ecosystems face significant damage from deforestation and environmental forest changes. We investigated the evolution of tree types of cover areas, deforested areas and total deforested areas from Curvature Carpathians using Gray-Level Co-occurrence Matrix and fractal analysis. The forest dynamics mapping was one of the main objectives of this study and it was carried out using multiple fractal and GLCM indices. We approached the analysis of satellite forest images by calculation of four fractal indices such as Pyramid dimension, Cube Counting Dimension, Fractal Fragmentation-Compaction Index and Tug-of-War lacunarity. We also calculated fractal dimension because it is an index of complexity comparing how the detail in a pattern changes with the scale at which it is measured. Fractal dimension is useful for estimation of irregularity or roughness of fractal and natural objects that do not conform to Euclidian geometry. While the fractal dimension quantifies how much space is occupied, the Tug-of-War lacunarity complements fractal dimension with its ability to quantify how space is occupied. Analysis was further supplemented by the Gray-Level Co-occurrence Matrix analysis because it quantifies spatial probability distributions of gray level values between pixel pairs within an image. The calculated Gray-Level Co-occurrence Matrix features included Angular Second Moment, Contrast, Correlation, Inverse Difference Moment and Entropy. Such comprehensive analysis has the advantage of combining fractal analysis that extracts quantitative information about the morphological complexity of the image with the spatial distribution of the gray pixel intensities as calculated by the co-occurrence features provided by Gray-Level Co-occurrence Matrix. Evolution of deforested areas, expansion of agricultural land and the increased demand for quality timber have affected the forests ecosystems and, the regional sustainable development of local communities.

Noise rejection and partial discharge source identification in insulation system under DC voltage supply

The problem to recognize the noise and identify the type of source generating discharges detected during campaigns of partial discharge measurements in an electrical apparatus is of utmost importance in the quality control, diagnostic, after laying testing and condition monitoring of DC insulation systems. This paper has the purpose to provide potential tools that are able to give considerable contribution into noise and partial discharge identification. In particular, the use of the T-F classification map, well assessed in AC, is able to cluster separately noise and discharges under DC supply as well. Then, simple algorithms involving the probability distribution of the amplitude values of the detected signals, as well as the recorded signal structure, could allow noise and PD identification, thus enabling noise rejection, and recognition and identification of the type of sources generating discharges.

Research on variable probability assignment technique of genetic algorithm for WTA of ground target attacking

The targets and the use of weapons are complicated on attacking ground target, Besides, the weapon-target assignment (WTA) research is extremely difficult and lacking. For a timely and rational WTA scheme can not only help to seize fleeting war opportunities, but also optimize the use of weapon resources to maximize the battlefield benefits with minimum costs, this article builds a mathematical model and uses genetic algorithm (GA) to find the optimal WTA result. But the algorithm is difficult to prepare better initial population because of the random assignment of variables which results in undesirable optimization results. To overcome the challenge in initializing GA, this article puts forward a variable probability assignment technique. This technique first uses feasible solutions to determine the probability distribution of the variable values, then, uses probability assignment mode to replace the stochastic uniform assignment mode to initialize variables, and produces the initial population individual close to the optimal individual with certainty. The simulation calculation shows that the improved GA can effectively solve the WTA problem of the large scale ground targets attacking with better performance.

Simple to Use Microsoft Excel Template for Estimating the Parameters of Some Selected Probability Distribution Model by Method of L-Moment

The focus of this research was to design a simple to use Microsoft excel algorithm that will aid in the estimation of the parameters of generalized extreme value probability distribution (GEV), generalized logistics probability distribution (GLO) and generalized pareto probability distribution (GPA), calculate the predicted rainfall/discharge based on L-moment procedures and compute the quantile estimates at various return periods.The algorithm was design based on the underlying mathematics of L-moment and has the capacity to handle forty (40) year’s annual maximum series of either rainfall or discharge data which must first be ranked in ascending order of magnitude. Basic descriptive statistics such as the sample mean, variance, standard deviation, skewness, kurtosis, coefficient of variation have been built into the algorithm. Other exciting features include; the computation of Probability weighted moment parameters (b0, b1, b2 and b3), L-Moment values (ƛ1, ƛ2, ƛ3 and ƛ4) , L-Moment ratio values (Ʈ2, Ʈ3 and Ʈ4), and goodness of fit statistics (RRMSE, RMSE, MAE, MADI and PPCC). Others include; the shape (k), scale (α) and location (ξ) parameters of GEV, GPA and GLO probability distributions. To test the performance of the algorithm, forty (40) year’s annual maximum rainfall data from Benin City was used. Basic time series analysis such as test of normality, test of homogeneity and outlier detection was conducted to ensure that the data used are adequate and suitable.Results obtained revealed that generalized logistics probability distribution GLO was the best fit distribution model for analyzing the annual maximum rainfall series at the study site. The predicted rainfall quantile magnitude (Qt) based on the GLO model ranges from 425.877mm at 2years return period to 762.759mm at 200years return period. The coefficient of determination (r 2 ) for the observed versus predicted rainfall based on the best fit model was observed to be 0.9793. It was thereafter concluded that L-moments and L –moment ratios are useful summary statistics for analyzing rainfall data. Keywords: L-moments, probability distribution, normality test, goodness of fit statistics, coefficient of variation. DOI : 10.7176/CER/11-9-05 Publication date :October 31 st 2019

Analysis of corrosion performance of rebar in Red mud blended concrete

In this paper, electrochemical technique was employed to evaluate the performance of Red mud (RM) on the reinforcement corrosion. This paper also reports the effect of chloride, sulphate and the combined chloride-sulphate solutions on the corrosivity of rebar embedded in Ordinary Portland Cement (OPC) and RM blended concrete (95% OPC & 5% RM) slab specimens. The corrosion performance was evaluated by Linear polarisation resistance sweep test on the reinforced slab specimens made with mix water contaminated with 5% NaCl, 2% MgSO4 and the combination of both salts. The corrosion performance was monitored for every 30 days over a period of 180 days, in terms of corrosion rate values. In order to investigate the overall performance of experimental test results they were analysed as per the specifications given by ASTM G16-13. The analysis of the corrosion data includes the descriptive statistics of the Normal, Weibull lognormal, and Smallest Extreme Value probability distribution functions (Pdfs) and the test of fit significance by the Anderson-Darling (AD) goodness of fit statistics. In addition, the analysis of variance was also carried out to determine the influence of each variable on the corrosion data. Further, the analysis of variance is also carried out to evaluate the influence of cementitious material and type of salt on corrosion data.

Equity Valuation: Forecasting Earnings Based on Probability Distributions Linked to Rating Categories

The paper continues an equity valuation model based on a random process modelling of earnings and book value, coupled with rating categories and rating migration. In essence, earnings and book value probability distributions are related to rating categories, and the probability of an issue to have a certain rating category at a certain time is calculated. Based on this, earnings are forecast as probability distributions. As reflected by the output distributions, in general, given its premises, the valuation model more realistically models inherent uncertainty, particularly increased uncertainty with time. It is noted that this approach to equity valuation is rather similar to reduced form models used with bond valuation. As a consequence, the probability of default is naturally incorporated into the valuation model. The necessary input earnings per book value, and book value growth, probability distributions are simulated, in accordance with preceding research, and the resultant output earnings, and book value, probability distributions are calculated and outlined.

Screen Content Compression Based on Enhanced Soft Context Formation

The compression of screen content has attracted the interest of researchers in the last years as the market for transferring data from computer displays is growing. It has already been shown that especially those methods can effectively compress screen content which are able to predict the probability distribution of next pixel values. This prediction is typically based on a kind of learning process. The predictor learns the relationship between probable pixel colours and surrounding texture. Recently, an effective method called ‘soft context formation’ (SCF) had been proposed which achieves much lower bitrates for images with less than 8 000 colours than other state-of-the-art compression schemes. This paper presents an enhanced version of SCF. The average lossless compression performance has increased by about 5% in application to images with less than 8 000 colours and about 10% for images with up to 90 000 colours. In comparison to FLIF, FP8v3, and HEVC (HM − 16.20 + SCM − 8.8), it achieves savings of about 33%, 4%, and 11% on average. The improvements compared to the original version result from various modifications. The largest contribution is achieved by the local estimation of the probability distribution for unpredictable colours in stage II of the compression scheme.