Characteristics Of Random Variables Research Articles

Survey on stochastic distribution systems: A full probability density function control theory with potential applications

AbstractComplex systems seen either in general engineering practice or economics are subjected to ever increased uncertainties that are mostly represented as random variables or parameters, and the characteristics of random variables are represented by their probability density functions (PDFs). Controlling their PDFs means to shape their stochastic distributions and in general it would provide a full treatment for system analysis and operational control and optimization. This leads to the development of stochastic distribution control (SDC) systems theory in the past decades, where the original aim of the controller design is to realize a shape control of the distributions of certain random variables in their PDFs sense for some engineering processes. Indeed, once the PDFs of these random variables or parameters are used to describe their distribution characters, the control task is to obtain control signals so that the output PDFs of stochastic systems are made to follow their target PDFs. The subject of SDC was initially originated for non‐Gaussian stochastic control systems design but has found a wide spectrum of applications in general systems in terms of data‐driven modeling, analysis, signal processing (filtering), data mining via multivariable statistics, decision‐making (optimization) for systems subjected to uncertainties and even in economics. In this context, SDC constitutes an effective primer tool for complex system analysis, control and operational optimizations. In this review paper, a detailed survey of the developments on the research of SDC systems will be made together with their wide spectrum applications and future perspectives.

The Unifying Frameworks of Information Measures

Information measures are capable of providing us with fundamental methodologies to analyze uncertainty and unveiling the substantive characteristics of random variables. In this paper, we address the issues of different types of entropies through q-generalized Kolmogorov-Nagumo averages, which lead to the propositions of the survival Rényi entropy and survival Tsallis entropy. Therefore, we make an inventory of eight types of entropies and then classify them into two categories: the density entropy that is defined on density functions and survival entropy that is defined on survival functions. This study demonstrates that, for each type of the density entropy, there exists a kind of the survival entropy corresponding to it. Furthermore, the similarity measures and normalized similarity measures are, respectively, proposed for each type of entropies. Generally, functionals of different types of information-theoretic metrics are equally diverse, while, simultaneously, they also exhibit some unifying features in all their manifestations. We present the unifying frameworks for entropies, similarity measures, and normalized similarity measures, which helps us deal with the available information measures as a whole and move from one functional to another in harmony with various applications.

Probabilistic Voltage Stability Analysis Based on Unscented Transformation and Maximum Entropy Principle

Considering the uncertainty of load and the random variation of wind farm output power in power system, a probabilistic voltage stability analysis method is proposed based on unscented transformation technique. According to the statistical characteristics of random variables in power system, the statistical characteristics of voltage stability margins, such as mean, standard deviation and moments, can be calculated by using a small number of samples and the conventional method. The maximum entropy method is applied to determine the probability distribution of voltage stability margin. In compared with Monte Carlo method, the effectiveness of the proposed method is verified on 39-bus and IEEE 57-bus system. The results show that the proposed method can accurately compute the statistical characteristics and the probability distribution of the voltage stability margin, and the computational efficiency is improved.

Solving Linear Unconstrained Problems of Combinatorial Optimization on Arrangements Under Stochastic Uncertainty

Linear unconstrained problem of combinatorial optimization on arrangements under stochastic uncertainty is being solved. The minimum is defined as the result of sequential comparison of numerical characteristics of random variables. The properties of the solution of the optimization problem under study are obtained. These properties use the properties of special constructed deterministic problems. The authors also propose the reduction method to solve linear unconstrained problem of combinatorial stochastic optimization, which is based on obtained solution's properties.

Reliability analysis of un-retrofitted and retrofitted concrete columns in Iran's building site conditions

The reliability analysis of built columns in Iran's building site conditions, un-retrofitted and retrofitted by CFRP, are compared with the target safety level of the Iranian Concrete Design Code and Code 345. Statistical characteristics of random variables in terms of resistance are found via field researches carried out on 60 active construction workshops and a total of 1,800 samples of concrete in Tehran and its suburbs. The results show that the CFRP materials can significantly increase the safety level of columns. Furthermore, the simulation results reveal that the safety levels of built concrete columns in Iran's building sites condition are lower than the desired level in the Iranian Concrete Design Code and Code 345. The results confirm the necessity of review on the partial safety coefficient of load and resistance in the Iranian codes. However, the results show that the target reliability index of un-retrofitted columns can significantly satisfied with the CFRP materials.

Some Problems of Statistics of Distribution Mixtures with Variable Concentrations

Some problems of estimating characteristics of random variables are considered. The observations used as a basis are a sample from a mixture of distributions, and the concentrations of components vary in the process of measurement. The distributions of components of the mixture are evaluated nonparametrically, while estimates for some functions of concentrations are both parametric and nonparametric. The estimates considered are proved to be consistent. Estimates are constructed on the basis of inhomogeneous empirical distribution functions.