Identification Of Probability Distribution Research Articles

Flood Frequency Analysis using L-Moment For Segamat River

Flood frequency analysis is critical in water system design and estimating flood recurrence. This study aims to conduct the flood frequency analysis on Segamat River streamflow site to find the optimum distribution that fits the flood frequency data. In terms of estimating parameters, the L-moment method is more robust and more efficient than the maximum likelihood method. Besides, the L-moment method is not affected by sampling variability. Therefore, in this study, we applied the technique of L-moment for parameter estimation on five candidate distributions, the generalised Pareto (GPA) distribution, generalised extreme value (GEV) distribution, generalised logistic (GLO) distribution, log-Pearson 3 (LP3) distribution, and log-normal (LN3) distribution. The rank score approach is implemented to determine the optimum distribution for the annual Segamat River peak flow. Probability distribution identification is essential and it is a fundamental step in statistical analysis. The goodness of fit test and efficiency assessment are employed to evaluate the distributions' performance. The results show that the LN3 distribution is selected as the optimum function for the yearly peak flow for the Segamat River streamflow site. The outcome of this study can be used to understand the flood frequency analysis for the Segamat River.

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Human-in-the-Loop Wireless Communications: Machine Learning and Brain-Aware Resource Management

Human-centric applications such as virtual reality and immersive gaming are central to future wireless networks. Common features of such services include: 1) their dependence on the human user’s behavior and state and 2) their need for more network resources compared to conventional applications. To successfully deploy such applications over wireless networks, the network must be made cognizant of not only the quality-of-service (QoS) needs of the applications, but also of the perceptions of the human users on this QoS. In this paper, by explicitly modeling the limitations of the human brain, a concrete measure for the delay perception of human users is introduced. Then, a learning method, called probability distribution identification, is developed to find a probabilistic model for this delay perception based on the brain features of a human user. Given the learned model for the delay perception of the human brain, a brain-aware resource management algorithm based on Lyapunov optimization is proposed for allocating radio resources to human users while minimizing the transmit power and taking into account the reliability of both machine type devices and human users. Then, a closed-form relationship between the reliability measure and wireless physical layer metrics of the network is derived. Simulation results show that a brain-aware approach can yield savings of up to 78% in power compared to the system that only considers QoS metrics. The results also show that, compared with QoS-aware, brain-unaware systems, the brain-aware approach can save substantially more power in low-latency systems.

Methods for identification of probability distribution of random variables from data samples with R statistical computing language

The following article discusses various methods for probability distribution fitting to simulated data by means of R statistical computing language. In particular, some graphical methods like plotting of histograms, empirical and theoretical density functions, P-P and Q-Q plots, were considered. Estimation functions for probability distribution parameters were investigated by applying method of moments, method of quantiles, method of maximum likelihood, and shortest distance method. Hypothesis about probability distribution were verifi ed with Kolmogorov–Smirnov, AIC, and BIC tests. The corresponding data set used to illustrate the above methods was taken from probability distribution of the maximum of Chenstov field restriction to a particular curve. The distribution was simulated with the special original algorithm in R statistical software.

Concrete meso-scale model with full set of 3D failure modes with random distribution of aggregate and cement phase. Part I: Formulation and numerical implementation

Prediction of failure mechanisms in concrete is a fairly complex task due to heterogeneous concrete microstructure, localization process triggered by cracks, multiple crack interactions during their growth and coalescence, and different dissipative mechanisms in a fracture process zone prior to localized failure and in a localization zone during the failure. None of the currently used phenomenological models can represent the full set of 3D failure modes. This work presents an attempt to solve this with the 3D meso-scale model based on discrete lattice approach. In particular we show that we can capture such complexities at the meso-scale, which is able to represent microcracks in fracture process zone along with the localized failure represented in terms of embedded strong discontinuity and accompanied with softening constitutive law. The model can also successfully simulate salient features of concrete response, such as order of magnitude of reduction in strength in uniaxial tension versus compression, strength increase in biaxial loading or hydrostatic tension. Moreover, macro-scale representation of failure surfaces obtained with presented model for different loading programs confirms the need for failure concrete criterion of multi-surface kind. Part I of this work presents the proposed meso-scale based on extensive number of numerical simulations with multiple realizations of different concrete specimens, along as the optimal deterministic fit for several common concrete failure models. The ultimate interest of the work is to provide detailed data set for different failure modes which can be used for identification of probability distribution of material parameters for different criteria. Such task is carried in Part II of this work.

On-line Full Probability Distribution Identification of ARX Model Parameters Based on Bayesian Approach

In this contribution, full probability distribution of parameters of ARX model is obtained for on-line problems by means of Bayesian approach and Markov chain Monte Carlo method (MCMC), which provides the ability to be applied on time-varying ARX models as well. Full probability distribution of parameters represent whole available knowledge of parameters. So, decision makers can follow any policies to make decision about point estimation, like dynamic point estimation. Moreover, the Bayesian approach has great potential in combining sources of knowledge much more easier. To decrease the computational efforts, full probability of model parameters are updated based on size-varying partitions. Furthermore, incorporating the posterior probability of previous partition into the jump probability of current partition, in MCMC method, improves the performance of the proposed algorithm from the computation and convergence rate point of view. Simulation results demonstrate the effectiveness and validity of the proposed algorithm.

An investigation on inter-individual variation in perceived discomfort of static posture holding.

Realizing population-level discomfort evaluation and control of common static posture holding tasks requires an understanding of the inter-individual variation in discomfort perception. However, little research is available. This study aimed to determine the types of mathematical probability distribution suitable for modeling population discomfort distributions of various static posture holding tasks and characterize how the magnitude of inter-individual variation in perceived discomfort varies across static posture holding tasks. Ten male and ten female subjects participated. The participants conducted static posture holding for a set of 180 short-duration (20-second-long) static posture holding tasks and subjectively rated the overall perceived discomfort for each task using the Borg CR-10 discomfort scale. Statistical analyses were conducted according to the study objectives. The static posture holding tasks exhibited multifarious discomfort distribution patterns. Probability distribution identification analyses indicated that no single distribution type could represent population discomfort distributions universally across different static posture holding tasks. Sample standard deviation of discomfort ratings data quantifying the magnitude of inter-individual variation in discomfort perception varied considerably across static posture holding tasks. It seemed to have a positive relationship with sample mean within the range of the experimental conditions. Population-level evaluation of discomforts associated with static posture holding tasks must be based on careful examinations of empirical discomfort distributions.

Review of Bayesian statistical analysis methods for cytogenetic radiation biodosimetry, with a practical example

Classical methods of assessing the uncertainty associated with radiation doses estimated using cytogenetic techniques are now extremely well defined. However, several authors have suggested that a Bayesian approach to uncertainty estimation may be more suitable for cytogenetic data, which are inherently stochastic in nature. The Bayesian analysis framework focuses on identification of probability distributions (for yield of aberrations or estimated dose), which also means that uncertainty is an intrinsic part of the analysis, rather than an 'afterthought'. In this paper Bayesian, as well as some more advanced classical, data analysis methods for radiation cytogenetics are reviewed that have been proposed in the literature. A practical overview of Bayesian cytogenetic dose estimation is also presented, with worked examples from the literature.

Estabelecimento de um plano de manutenção baseado em análises quantitativas no contexto da MCC em um cenário de produção JIT

Este artigo apresenta um método para desenvolver análises quantitativas que orientem a revisão ou elaboração de um plano de manutenção de equipamentos em um cenário de produção just in time. O método proposto contempla: i) Identificar os conjuntos que influenciam a confiabilidade; ii) Levantar taxas de falhas; iii) Classificar os conjuntos quanto ao efeito de suas falhas; iv) Levantar parâmetros de demanda da linha; v) Identificar as distribuições de probabilidade da demanda da linha e dos tempos de bom funcionamento e tempos de reparo dos conjuntos; vi) Simular a produção/manutenção utilizando o método de Monte Carlo; vii) Realizar uma análise de sensibilidade a eventuais variações na demanda, MTBF e MTTR; e viii) Estabelecer a estratégia de manutenção e intervalos entre manutenções preventivas. A aplicação do método é ilustrada através de um estudo real realizado em uma linha de rotulagem e enchimento de galões de uma empresa do setor de tintas e corantes. A aplicação do método permitiu identificar com clareza os conjuntos e subconjuntos críticos frente ao cenário produtivo em questão.

Offshore wind turbine maintenance access: a closed‐form probabilistic method for calculating delays caused by sea‐state

ABSTRACTOffshore wind energy is fast developing and with it a growing understanding of the challenge to maintain high levels of turbine availability and to keep down maintenance costs. Loss of turbine availability is, of course, related to component failure rate but is also highly dependent on access to the turbine, and this in turn reflects the wind and sea conditions occurring at the site as well as the operational limits of the vessels and plant being used.A computational approach has been developed on the basis of probability calculations, enabling very fast estimates to be made of offshore access probabilities and expected delays. These can be used directly to explore the impact of different parameters such as key component reliability, time to repair and access constraints at specific offshore sites. The methodology used is derived and explained in detail. Different numerical techniques are available to calculate the probability distributions and their parameters as required by the methodology. These are presented and contrasted. Example applications of the methodology are provided for two specific sites that provide a degree of validation and also allow comparison of the different numerical approaches to probability distribution identification. It is shown that the accessibility calculated using the developed method is believable in the context of operational access data for the sites in question. Copyright © 2012 John Wiley & Sons, Ltd.

Partial identification using random set theory

This paper illustrates how the use of random set theory can benefit partial identification analysis. We revisit the origins of Manski’s work in partial identification (e.g., Manski (1989, 1990)) focusing our discussion on identification of probability distributions and conditional expectations in the presence of selectively observed data, statistical independence and mean independence assumptions, and shape restrictions. We show that the use of the Choquet capacity functional and the Aumann expectation of a properly defined random set can simplify and extend previous results in the literature. We pay special attention to explaining how the relevant random set needs to be constructed, depending on the econometric framework at hand. We also discuss limitations in the applicability of specific tools of random set theory to partial identification analysis.

Srovnání volatility akciových indexů PX a FTSE 100

The article deals with a typical phenomenon of financial time series - volatility. These time series usually embody intermittent periods of relative calm and quite high variability. A volatility modelling of time series is made with the help of special econometric volatility models which characterize the so-called conditional heteroskedasticity. The goal of this paper is to choose a suitable volatility model for Prague PX Index and London FTSE 100. The path to the aim is via a stationarity analysis of tracked time series of closing values of the mentioned indexes, conditional heteroskedasticity and autocorrelation tests and an identification of probability distribution of the studied quantity. A profiling of asymmetric effects is also very important because they determine the linear or nonlinear character of the resulting model.

논 유출수 BOD의 유량가중평균농도(EMC) 확률분포

Identification of probability distribution for water quality constituents from specific land use is important to achieve successful implementation of TMDL program. In this 3-year study, distribution of discharge and BOD(Biological Oxygen Demand) concentration from paddy rice fields were monitored. Four probability distributions, normal, log-normal, Gamma and Weibull were fitted and the goodness-of-fit was assessed using probability plots and Kolmogorov-Smirnov test. <TEX>$EMC_s$</TEX> of BOD in runoff from paddy field ranged 0.37 to <TEX>$7.99\;mgL^{-1}$</TEX>, and all four probability distributions were acceptable. But the normal distribution would be preferred for BOD from paddy fields considering nature of straight forward application.

Likelihood-based confidence sets for partially identified parameters

There has been growing interest in partial identification of probability distributions and parameters. This paper considers statistical inference on parameters that are partially identified because data are incompletely observed, due to nonresponse or censoring, for instance. A method based on likelihood ratios is proposed for constructing confidence sets for partially identified parameters. The method can be used to estimate a proportion or a mean in the presence of missing data, without assuming missing-at-random or modeling the missing-data mechanism. It can also be used to estimate a survival probability with censored data without assuming independent censoring or modeling the censoring mechanism. A version of the verification bias problem is studied as well.

Partial identification of probability distributions with misclassified data

This paper addresses the problem of data errors in discrete variables. When data errors occur, the observed variable is a misclassified version of the variable of interest, whose distribution is not identified. Inferential problems caused by data errors have been conceptualized through convolution and mixture models. This paper introduces the direct misclassification approach. The approach is based on the observation that in the presence of classification errors, the relation between the distribution of the ‘true’ but unobservable variable and its misclassified representation is given by a linear system of simultaneous equations, in which the coefficient matrix is the matrix of misclassification probabilities. Formalizing the problem in these terms allows one to incorporate any prior information into the analysis through sets of restrictions on the matrix of misclassification probabilities. Such information can have strong identifying power. The direct misclassification approach fully exploits it to derive identification regions for any real functional of the distribution of interest. A method for estimating the identification regions and construct their confidence sets is given, and illustrated with an empirical analysis of the distribution of pension plan types using data from the Health and Retirement Study.

Providing Unified Measurements in Checking Measuring Instruments

A method is considered for calculating the basic error of a measuring instrument from test data by the employment of structural and parametric identification of probability distributions on the criterion for maximum reproducibility.

The Identification of Probability Distributions

A method for the parametric identification of probability distributions with respect to the statistical distribution of measurement data, based on a rigorous determination of the probability of agreement is described.

Statistics and GIS in environmental geochemistry — some problems and solutions

Statistics and geographical information system (GIS) are receiving more and more attention in environmental geochemistry. However, it is important to know the functions and limitations, the advantages and disadvantages of these techniques for better understanding of their applications. Univariate statistics is useful for mean calculation, identification of probability distribution and outlier detection. Multivariate analysis plays an important role in the study of relationships among variables. However, while dealing with regionalized variables in environmental geochemistry, the conventional statistics show their shortcomings as they are based on some kind of assumptions for random variables. Spatial analysis makes use of the spatial coordinate information of the variables, and also takes the spatial correlation into consideration. However, these pure mathematical methods are still unsatisfactory as the nature of environmental geochemistry is far from being so simple. GIS provides visualization and some spatial analysis functions with much spatial information involved. An expert system is useful for classification and prediction based on various types of information. However, the rule base for expert systems in environmental geochemistry is too small, and needs to be developed. Problems and possible solutions with the application of statistics and GIS in environmental geochemistry are discussed. Examples are based on the authors' experiences in the Yangtze River basin, China, and in southeastern Sweden. Several ideas are discussed in this paper. A `robust-symmetric mean' proposed by the authors is one of the best methods for mean calculation. For the probability distribution of trace elements, the widely accepted `log-normal distribution' is only a special case of `positively skewed distributions' which is more adequate. The combination of univariate methods and PCA is used to detect outlying samples. Partial least square (PLS) regression, principal component analysis (PCA), cluster analysis, discriminant analysis and expert systems may be used to differentiate anthropogenic anomalies from the natural background. Spatial correlations among environmental geochemical variables are revealed by cross-variograms. An environmental information system, with the integration of statistics, GIS, expert systems and environmental models should be established to further the study in environmental geochemistry, as well as to provide decision support.