Probability density function

About: Probability density function is a research topic. Over the lifetime, 22321 publications have been published within this topic receiving 422885 citations. The topic is also known as: probability function & PDF.

An identification of Energy Cascade in Turbulence by Orthonormal Wavelet Analysis

Abstract: Orthonormal wavelet expansion method is applied to an analysis of atmospheric turbulence data which shows more than two decades of the inertial subrange spectrum. The result of the orthonor­ mal wavelet analysis of the turbulence data is discussed in comparison with those of an artificial random noise. The local wavelet spectra of turbulence show a characteristic structure. which is absent in the artificial random noise and is identified with the trace of the energy cascade process. The higher· order structure function of velocity. obtained by the wavelet analysis. shows the intermit· tent structure of the flow field. In 1941 Kolmogorov proposed a universal theory of fluid turbulence/) in which every statistical quantity concerning the inertial subrange of flow field is assumed to be determined only by the energy dissiation rate. According to this theory, the average of the n-th order of velocity difference between two points separated by spatial distance r is proportional to r"13. This prediction has been repeatedly examined in accurate experiments in high Reynolds number flows, and it is now widely accepted that as far as lower order of velocity difference is concerned, the r-dependence agrees well with the Kolmogorov theory. In particular, experimental forms of the energy spectrum of the velocity field, which corresponds to n=2, coincide with the Kolmogorov form of k- 5/3 • However, it has been repeatedly confirmed that higher order of the velocity difference has a statistical property different from Kolmogorov's prediction, so that the n-th order structure function of the velocity field, when normalized by the second order of the velocity difference, shows a clear r-dependence. This fact implies that the energy cascade process in the inertial subrange has an unnegligible deviation from the Kolmogorov picture. The deviation is reflected in the shape of the probability distribution function of the velocity difference, which has longer tail for smaller distance r. This deviation is often called intermittency, and its characterization is regarded as one of the central problems of fluid turbulence. The fact that intermittency becomes more prominent at smaller scales indicates that the intermittency is an essential part of the energy cascade process. However, this cascade process itself, sometimes called Richardson cascade, has been only a matter of theoretical consideration, and its characteristic structure has not yet been clearly captured in experiments or in numerical simula­ tions.

Probabilistic Load Flow Modeling Comparing Maximum Entropy and Gram-Charlier Probability Density Function Reconstructions

Abstract: Probabilistic load flow (PLF) modeling is gaining renewed popularity as power grid complexity increases due to growth in intermittent renewable energy generation and unpredictable probabilistic loads such as plug-in hybrid electric vehicles (PEVs). In PLF analysis of grid design, operation and optimization, mathematically correct and accurate predictions of probability tail regions are required. In this paper, probability theory is used to solve electrical grid power load flow. The method applies two Maximum Entropy (ME) methods and a Gram-Charlier (GC) expansion to generate voltage magnitude, voltage angle and power flow probability density functions (PDFs) based on cumulant arithmetic treatment of linearized power flow equations. Systematic ME and GC parameter tuning effects on solution accuracy and performance is reported relative to converged deterministic Monte Carlo (MC) results. Comparing ME and GC results versus MC techniques demonstrates that ME methods are superior to the GC methods used in historical literature, and tens of thousands of MC iterations are required to reconstitute statistically accurate PDF tail regions. Direct probabilistic solution methods with ME PDF reconstructions are therefore proposed as mathematically correct, statistically accurate and computationally efficient methods that could be applied in the load flow analysis of large-scale networks.

The Odd Lindley-G Family of Distributions

Abstract: We propose a new generator of continuous distributions with one extra positive parameter called the odd Lindley-G family. Some special cases are presented. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Various structural properties of the new family, which hold for any baseline model, are derived including explicit expressions for the quantile function, ordinary and incomplete moments, generating function, Renyi entropy, reliability, order statistics and their moments and k upper record values. We discuss estimation of the model parameters by maximum likelihood and provide an application to a real data set.

Fractional Fokker-Planck dynamics: Numerical algorithm and simulations.

Abstract: Anomalous transport in a tilted periodic potential is investigated numerically within the framework of the fractional Fokker-Planck dynamics via the underlying continuous-time random walk. An efficient numerical algorithm is developed which is applicable for an arbitrary potential. This algorithm is then applied to investigate the fractional current and the corresponding nonlinear mobility in different washboard potentials. Normal and fractional diffusion are compared through their time evolution of the probability density in state space. Moreover, we discuss the stationary probability density of the fractional current values.

Probability Density of the Received Power in Mobile Networks

Abstract: Probability density of the received power is well analyzed for wireless networks with static nodes. However, most of the present days networks are mobile and not much exploration has been done on statistical analysis of the received power for mobile networks in particular, for the network with random moving patterns. In this paper, we derive probability density of the received power for mobile networks with random mobility models. We consider the power received at an access point from a particular mobile node. Two mobility models are considered: Random Direction (RD) model and Random way-point (RWP) model. Wireless channel is assumed to have a small scale fading of Rayleigh distribution and path loss exponent of 4. 3D, 2D and 1D deployment of nodes are considered. Our findings show that the probability density of the received power for RD mobility models for all the three deployment topologies are weighted confluent hypergeometric functions. In case of RWP mobility models, the received power probability density for all the three deployment topologies are linear combinations of confluent hypergeometric functions. The analytical results are validated through NS2 simulations and a reasonably good match is found between analytical and simulation results.