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Interval Estimation of the probability distribution function

OPTOELECTRONICS INSTRUMENTATION AND DATA PROCESSING 2015年第2期51卷 120-123页

作者： Kuleshov, E. L. Far Eastern Fed Univ Ul Sukhanova 8 Vladivostok 690950 Russia

The Moivre - Laplace asymptotics is used to construct an interval estimate of the probability distribution function that is an interval with random boundaries, which covers the true value of the distribution function with a given confidence factor. It is shown that the use of the asymptotic instead of a binomial probability distribution results in an error whose value is tolerable for small sampling sizes and monotonically reduces with decreases sampling size.

关键词： interval estimate probability distribution function confidence factor goodness-of-fit test statistical hypothesis

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probability distribution function FOR THE EUCLIDEAN DISTANCE BETWEEN TWO TELEGRAPH PROCESSES

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ADVANCES IN APPLIED probability 2014年第4期46卷 1172-1193页

作者： Kolesnik, Alexander D. Moldavian Acad Sci Inst Math & Comp Sci Kishinev 2028 Moldova

Consider two independent Goldstein-Kac telegraph processes X-1(t) and X-2(t) on the real line R. The processes X-k(t), k = 1, 2, describe stochastic motions at finite constant velocities c(1) > 0 and c(2) > 0 that start at the initial time instant t = 0 from the origin of R and are controlled by two independent homogeneous Poisson processes of rates lambda(1) > 0 and lambda(2) > 0, respectively. We obtain a closed-form expression for the probability distribution function of the Euclidean distance rho(t) = vertical bar X-1(t) - X-2(t)vertical bar, t > 0, between these processes at an arbitrary time instant t > 0. Some numerical results are also presented.

关键词： Telegraph process telegraph equation persistent random walk probability distribution function Euclidean distance

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A Novel Methodology to Estimate probability Density function of Voltage Sag Duration and Failure Rates on Power distribution Systems

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IEEE ACCESS 2023年 11卷 16863-16874页

作者： Cebrian, Juan C. Giacomini Jr, Jairo Carneiro, Carlos A. Silva, Gabriela B. Morales-Paredes, Helmo K. Sao Paulo State Univ UNESP Inst Sci & Engn BR-18409010 Itapeva SP Brazil Sao Paulo State Univ UNESP Inst Sci & Technol BR-18087180 Sorocaba SP Brazil

Voltage sags and power interruptions are important power quality problems that affect sensitive customers, mainly because they cause annual massive economical losses to the industrial sector as a result of unexpected production process disruptions. In this sense, to propose corrective and preventive measures and improve the power quality of the distribution systems, stochastic methodologies have been proposed in the literature to estimate annual voltage sags and power interruptions. However, these methodologies, generally, use typical cumulative distribution functions of voltage sag duration (PSgD), which may not reflect the real estate of the network under study. To solve this constraint, this paper proposes a novel methodology to estimate a proper PSgD considering information of the distribution network (i.e., topology and coordination schemes of the protection system) and the stochastic behaviors of short-circuits that can affect the distribution system. Moreover, the proposed methodology allows estimating permanent failure rates and average repair time considering known or expected values of reliability indicators. The results show that this proposed methodology is capable to adapt from an initial PSgD curve to another one with fidelity, in order to achieve real values of expected annual power interruptions.

关键词： distribution networks power interruption probability distribution function reliability indicators voltage sag

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probability distribution functions of Velocity Fluctuations and Quadrant Analysis on Turbulent Flow Around a Horizontal Cylinder Across a Channel Bed

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WATER 2025年第7期17卷 958-958页

作者： Kumar, Sandeep Kumar, Bimlesh Pu, Jaan H. Hanmaiahgari, Prashanth Reddy Indian Inst Technol Dept Civil Engn Kharagpur 721302 India Indian Inst Technol Guwahati Dept Civil Engn Gauhati 781039 India Univ Bradford Fac Engn & Digital Technol Bradford BD7 1DP England

An experiment is conducted to investigate the turbulent flow field close to a wall-fastened horizontal cylinder. The evolution of the flow field is analyzed by evaluating turbulent flow characteristics and fluid dynamics along the lengthwise direction. The approach flow velocity retards in the immediate upstream area of the cylinder. At the crest level of the cylindrical pipe, the turbulence characteristics such as Reynolds stresses and turbulence intensities are attaining their peaks. Gram-Charlier (GC) series-based Hermite polynomials yield probability density functions that better match experimental data than those from Gram-Charlier (GC) series-based exponential distributions, demonstrating the superiority of the Hermite polynomial method. Quadrant analysis reveals that sweeps (Q4) dominate intermediate and free-surface zones, while ejections (Q2) prevail near the bed, both being primary contributors to Reynolds shear stress (RSS). The stress component remains minimal or zero for all events when hole size H >= six. Larger hole sizes (>= five) drastically reduced the stress fraction, approaching zero. The stress fraction was highest near the cylinder, decreasing with distance and eventually plateauing. The study enhances the understanding of flow hydraulics around cylindrical objects in rough-bed natural streams.

关键词： probability distribution function Gram-Charlier Hermite polynomials bursting events turbulence

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Predictions of the solar wind speed by the probability distribution function model

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SPACE WEATHER-THE INTERNATIONAL JOURNAL OF RESEARCH AND APPLICATIONS 2014年第6期12卷 337-353页

作者： Bussy-Virat, C. D. Ridley, A. J. Univ Michigan Dept Atmospher Ocean & Space Sci Ann Arbor MI 48109 USA

The near-Earth space environment is strongly driven by the solar wind and interplanetary magnetic field. This study presents a model for predicting the solar wind speed up to 5 days in advance. probability distribution functions (PDFs) were created that relate the current solar wind speed and slope to the future solar wind speed, as well as the solar wind speed to the solar wind speed one solar rotation in the future. It was found that a major limitation of this type of technique is that the solar wind periodicity is close to 27 days but can be from about 22 to 32 days. Further, the optimum lag between two solar rotations can change from day to day, making a prediction of the future solar wind speed based solely on the solar wind speed approximately 27 days ago quite difficult. It was found that using a linear combination of the solar wind speed one solar rotation ago and a prediction of the solar wind speed based on the current speed and slope is optimal. The linear weights change as a function of the prediction horizon, with shorter prediction times putting more weight on the prediction based on the current solar wind speed and the longer prediction times based on an even spread between the two. For all prediction horizons from 8 h up to 120 h, the PDF Model is shown to be better than using the current solar wind speed (i.e., persistence), and better than the Wang-Sheeley-Arge Model for prediction horizons of 24 h.

关键词： probability distribution function

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probability distribution function of the order parameter: Mixing fields and universality

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COMPUTER PHYSICS COMMUNICATIONS 2013年第2期184卷 259-269页

作者： Plascak, J. A. Martins, P. H. L. Univ Fed Minas Gerais Dept Fis Inst Ciencias Exatas BR-30123970 Belo Horizonte MG Brazil Univ Georgia Ctr Simulat Phys Athens GA 30602 USA Univ Fed Mato Grosso Inst Fis Cuiaba MT Brazil

We briefly review the use of the order parameter probability distribution function as a useful tool to obtain the critical properties of statistical mechanical models using computer Monte Carlo simulations. Some simple discrete spin magnetic systems on a lattice, such as Ising, general spin-S Blume-Capel and Baxter-Wu, Q-state Potts, among other models, will be considered as examples. The importance and the necessity of the role of mixing fields in asymmetric magnetic models will be discussed in more detail, as well as the corresponding distributions of the extensive conjugate variables. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Multicritical points probability distribution function Monte Carlo simulations Mixing fields

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Rupture of single receptor-ligand bonds: A new insight into probability distribution function

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COLLOIDS AND SURFACES B-BIOINTERFACES 2013年 101卷 501-509页

作者： Gupta, V. K. Univ Maryland Baltimore Cty Baltimore MD 21250 USA

Single molecule force spectroscopy is widely used to determine kinetic parameters of dissociation by analyzing bond rupture data obtained via applying mechanical force to cells, capsules, and beads that are attached to an intermolecular bond. The current analysis assumes that the intermolecular bond force is equal to the externally applied mechanical force. We confirm that viscous drag alone or in combination with cellular deformation resulting in viscoelasticity modulates bond force so that the instantaneous intermolecular bond force is not equivalent to the applied force. The bond force modulation leads to bond rupture time and force histograms that differ from those predicted by probability distribution function (PDF) using the current approach. A new methodology that accounts for bond force modulation in obtaining PDF is presented. The predicted histograms from the new methodology are in excellent agreement with the respective histograms obtained from Monte Carlo simulation. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Cellular adhesion Cellular deformation Bond force modulation probability distribution function Kinetic off-rate

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probability distribution functions for service loads of frame scaffoldings

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BULLETIN OF THE POLISH ACADEMY OF SCIENCES-TECHNICAL SCIENCES 2021年第2期69卷

作者： Blazik-Borowa, Ewa Pienko, Michal Szer, Iwona Hola, Bozena Czarnocki, Krzysztof Lublin Univ Technol Fac Civil Engn & Architecture Nadbystrzycka 40 PL-20618 Lublin Poland Lodz Univ Technol Fac Civil Engn Architecture & Environm Engn Politech 6 PL-90924 Lodz Poland Wroclaw Univ Sci & Technol Fac Civil Engn Wybrzeze Wyspianskiego 27 PL-50370 Wroclaw Poland Lublin Univ Technol Fac Management Nadbystrzycka 38 PL-20618 Lublin Poland

The paper discusses service load measurements (weight of construction materials, small equipment and workers) conducted on 120 frame scaffoldings all over Poland in 2016-2018. Despite the fact that the scaffolding should ensure the safety of its users, most accidents on construction sites are caused by fall from height. Service loads are one of the elements affecting the safety of scaffolding use. On the basis of the studies, maximum load on one platform and maximum load on a vertical scaffolding module for one day were obtained. They were treated as the random variables of the maximum values. Histograms and probability density functions were determined for these variables. The selection of a probability distribution consisted in the selection of a probability density function by means of fitting curves to the study result histograms using the method of least squares. The analysis was performed for distribution Weibull and Gumbel probability density functions which are applied for maximum values of random variables. Parameters of these functions can be used for the purposes of the reliability analysis to calibrate partial safety factors in simulation of service load during the scaffolding failure risk assessment. Besides, the probability of not exceeding the standard loads provided for frame scaffoldings for 120 weeks was established on the aforementioned basis. The results of the presented research show that in Poland there is a high probability of exceeding the permissible service loads in one year and thus there is a high risk of scaffolding damage.

关键词： scaffolding service load extreme events probability distribution function safety

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A note on the probability distribution function of the surface electromyogram signal

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BRAIN RESEARCH BULLETIN 2013年第1期90卷 88-91页

作者： Nazarpour, Kianoush Al-Timemy, Ali H. Bugmann, Guido Jackson, Andrew Newcastle Univ Inst Neurosci Newcastle Upon Tyne NE1 7RU Tyne & Wear England Univ Plymouth CRNS Plymouth PL4 8AA Devon England

The probability density function (PDF) of the surface electromyogram (EMG) signals has been modelled with Gaussian and Laplacian distribution functions. However, a general consensus upon the PDF of the EMG signals is yet to be reached, because not only are there several biological factors that can influence this distribution function, but also different analysis techniques can lead to contradicting results. Here, we recorded the EMG signal at different isometric muscle contraction levels and characterised the probability distribution of the surface EMG signal with two statistical measures: bicoherence and kurtosis. Bicoherence analysis did not help to infer the PDF of measured EMG signals. In contrast, with kurtosis analysis we demonstrated that the EMG PDF at isometric, non-fatiguing, low contraction levels is super-Gaussian. Moreover, kurtosis analysis showed that as the contraction force increases the surface EMG PDF tends to a Gaussian distribution. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Electromyogram signal Higher order statistics probability distribution function

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Monte Carlo method for evaluation of surface emission rate measurement uncertainty

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Nuclear Science and Techniques 2024年第7期35卷 126-136页

作者： Yuan-Qiao Li Min Lin Li-Jun Xu Rui Luo Yu-He Zhang Qian-Xi Ni Yun-Tao Liu China Institute of Atomic Energy Beijing102413China National Key Laboratory for Metrology and Calibration Techniques Beijing102413China Department of Radiation Oncology Hunan Cancer HospitalChangsha410031China The Affiliated Cancer Hospital of Xiangya School of Medicine Central South UniversityChangsha410031China

The aim of this study is to evaluate the uncertainty of 2πα and 2πβ surface emission rates using the windowless multiwire proportional counter *** study used the Monte Carlo method (MCM) to validate the conventional Guide to the Expression of Uncertainty in Measurement (GUM) method.A dead time measurement model for the two-source method was established based on the characteristics of a single-channel measurement system,and the voltage threshold correction factor measurement function was indirectly obtained by fitting the threshold correction *** uncertainty in the surface emission rate was calculated using the GUM method and the law of propagation of *** MCM provided clear definitions for each input quantity and its uncertainty distribution,and the simulation training was realized with a complete and complex mathematical *** results of the surface emission rate uncertainty evaluation for four radioactive plane sources using both methods showed the uncertainty’s consistency E_(n)<0.070 for the comparison of each source,and the uncertainty results of the GUM were all lower than those of the ***,the MCM has a more objective evaluation process and can serve as a validation tool for GUM results.

关键词： Surface emission rate Monte Carlo method Metrology probability distribution function Dead time Low-energy loss correction Least-squares method

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