Variance Of Random Variables Research Articles

DPIM-based global reliability analysis method for the cable-stayed bridges and the determination of global target reliability index

This study presents an approach to analyzing the dynamic global reliability of cable-stayed bridges using the direct probability integral method. The analysis considers the degradation of resistance in the concrete main beam, tower, and cables, as well as the time-varying nature of the load effect. Six types of limit state functions for failure modes are established, including bending failure of the beam, static torsional failure of the beam, wind vibration failure of the beam, transverse buckling failure of the tower, longitudinal strength failure of the tower, and strength failure of the stay cable due to fretting fatigue and corrosion. A time-dependent extreme value mapping is constructed in the time domain, then the joint probability density integral equation of time-varying extreme value mapping of multiple performance functions is established. According to the mean and variance of random variables in the evaluation reference period, the direct probability integral method with Heaviside function (DPIM-H) is employed to solve the equation, and the dynamic global reliability index of cable-stayed bridge is obtained. As an example, the Brotonne cable-stayed bridge’s global reliability is analyzed, and the reasonable value of the global target reliability index is studied considering the structural performance degradation.

A Method of Value Measurement Based on Probability Theory in Economics

Value is one of the most fundamental concepts in economics. The existing main definitions of value have certain limitations and are difficult to be unified and quantified. Thus, this article presents a method of quantifying value based on the conditional probability theory; we set value as a random variable,a price is the value of the good in terms of money, according to the price’s historical records, quantitative statistics and human experiences, and thus uses conditional probability distribution to measure value. Furthermore, the mean and variance of random variables are used to describe the weighted average of the possible values and the dispersion of values distribution. This method provides a new perspective for the measurement of value.

A Method of Value Measurement Based on Probability Theory in Economics

Value is one of the most fundamental concepts in economics. The existing main definitions of value have certain limitations and are difficult to be unified and quantified. Thus, this article presents a method of quantifying value based on the conditional probability theory; we set value as a random variable,a price is the value of the good in terms of money, according to the price’s historical records, quantitative statistics and human experiences, and thus uses conditional probability distribution to measure value. Furthermore, the mean and variance of random variables are used to describe the weighted average of the possible values and the dispersion of values distribution. This method provides a new perspective for the measurement of value.

Some new findings on the cumulative residual Tsallis entropy

Several generalizations of Shannon entropy have been introduced in the literature. One of such a measure is the cumulative residual Tsallis entropy (CRTE) which can be viewed as an alternative dispersion measure. In this paper, we obtain some further results for such a measure, in relation with the cumulative residual Tsallis entropy and with the variance of random variables. Specifically, we present new equivalent expressions, bounds, normalized CRTE, connection to the differential entropy and excess wealth transform and stochastic comparisons involving such measures. Besides, the dynamic version of such under consideration measure is elaborated and some monotonicity results are also given. Finally, we consider the problem of estimating the CRTE by means of the empirical CRTE. In this regard, we use two different empirical estimators of cumulative distribution function to estimate CRTE. Then, we study practical results of the second estimator in blind image quality assessment.

On some forms of registration and display of modes of operation of vehicles

The article discusses the shortcomings of existing methods of accounting for engine operating time for the purpose of forming standards and modes of maintenance and repair. The results of testing a vehicle using specialized tools, including an adapter to the OBD diagnostic connector and a smartphone with special software, which allows registering, storing and accumulating data on the speed and load modes of the engine and the car, are presented. According to the test results, the drawbacks of registering the parameters of speed and load modes are analyzed by traditional characteristics in the form of mathematical expectation and variance of random variables. Methods of formalized display of the character of parameter changes in time are considered using autocorrelation functions and matrices of transition probabilities. The results of testing the analysis of the nature of changes in operating parameters in urban and mainline operating conditions are presented.

Quantifying networks complexity from information geometry viewpoint

We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as weighted edges among vertices. We then associate to the parameter space a statistical manifold endowed with a Riemannian metric structure (that of Fisher-Rao). Going on, in analogy with the microcanonical definition of entropy in Statistical Mechanics, we introduce an entropic measure of networks complexity. We prove that it is invariant under networks isomorphism. Above all, considering networks as simplicial complexes, we evaluate this entropy on simplexes and find that it monotonically increases with their dimension.

Risk Factor Based Design of Cantilever Retaining Walls

Sensitivity analysis of geotechnical random variables on potential failure modes (overturning, sliding, bearing capacity and eccentricity) of a cantilever retaining wall reveals that high sensitivity of a particular variable on a particular mode of failure does not necessarily imply a remarkable contribution to the overall failure probability. The present paper aims to combine probability of failure (P f ) of each failure mode and sensitivity of the random variables to these failure modes and introduces a new factor, called Probabilistic Risk Factor (R f ) for each random variable. P f is calculated by Monte Carlo Simulation and sensitivity analysis of each random variable is calculated based on normalized F-Statistics value. R f is a reduction factor which takes into account the variations of random variables and hence can be directly implemented in design by the designers. The random variables (friction angle and unit weight of backfill soil; and friction angle, unit weight and cohesion of foundation soil), when divided by R f and applied in design, yield a structure which is safe against variations of the random variables. It is observed that R f of friction angle (φ 1 ) of backfill increases and cohesion (c 2 ) of foundation soil decreases with an increase in variation of φ 1 , while R f for unit weights (γ 1 and γ 2 ) of both the soil and friction angle of foundation soil (φ 2 ) remains almost constant. Finally, design guidelines for different variations of φ 1 are provided based on the proposed methodology, which proves to be cost effective.

Estimation of Random Variable Distribution Parameters by the Monte Carlo Method

Abstract The paper is concerned with issues of the estimation of random variable distribution parameters by the Monte Carlo method. Such quantities can correspond to statistical parameters computed based on the data obtained in typical measurement situations. The subject of the research is the mean, the mean square and the variance of random variables with uniform, Gaussian, Student, Simpson, trapezoidal, exponential, gamma and arcsine distributions.

Reliability Coupled Sensitivity Based Design Approach for Gravity Retaining Walls

Sensitivity analysis involving different random variables and different potential failure modes of a gravity retaining wall focuses on the fact that high sensitivity of a particular variable on a particular mode of failure does not necessarily imply a remarkable contribution to the overall failure probability. The present paper aims at identifying a probabilistic risk factor (R f ) for each random variable based on the combined effects of failure probability (P f ) of each mode of failure of a gravity retaining wall and sensitivity of each of the random variables on these failure modes. P f is calculated by Monte Carlo simulation and sensitivity analysis of each random variable is carried out by F-test analysis. The structure, redesigned by modifying the original random variables with the risk factors, is safe against all the variations of random variables. It is observed that R f for friction angle of backfill soil (φ 1 ) increases and cohesion of foundation soil (c 2 ) decreases with an increase of variation of φ 1 , while R f for unit weights (γ 1 and γ 2 ) for both soil and friction angle of foundation soil (φ 2 ) remains almost constant for variation of soil properties. The results compared well with some of the existing deterministic and probabilistic methods and found to be cost-effective. It is seen that if variation of φ 1 remains within 5 %, significant reduction in cross-sectional area can be achieved. But if the variation is more than 7–8 %, the structure needs to be modified. Finally design guidelines for different wall dimensions, based on the present approach, are proposed.

Find multi-objective paths in stochastic networks via chaotic immune PSO

Path finding is a fundamental research topic in transportation planning, intelligent transportation system, routine selection, etc. It is usually simplified as the shortest path (SP) in deterministic networks. However, some parameters in real life are stochastic. In this article, a more pragmatic model for stochastic networks was proposed, which not only considers determinist variables but also the mean and variances of random variables. In order to fasten the solution of our model, a novel method was proposed, which combines artificial immune system (AIS), chaos operator, and particle swarm optimization (PSO). Numerical experiments were presented to demonstrate that this proposed model is valid, effective, and more close to real-life, and CIPSO outperforms GA and PSO in respect of route optimality and convergence time.

Sharp mean-variance bounds for Jensen-type inequalities

We give a short proof of a Jensen-type inequality involving the mean and variance of random variables and valid for a class of functions having a convexity-like property. A number of applications are presented which illustrate the applicability of the result.