Statistical Probability Density Functions Research Articles

Physical layer security in SWIPT-based cooperative vehicular relaying networks

The future of autonomous transportation systems depends on energy sustainability and secure information exchange from low-power vehicular sensors, hence the increased interest in vehicular sensor charging using simultaneous wireless information and power transfer (SWIPT). This study investigates the physical layer security of a SWIPT-based radio frequency energy harvesting cooperative vehicular relaying network subjected to cascade Nakagami-m and double Nakagami-m (DN) fading channels. In the considered system model, a stationary source communicates with a mobile destination through a power-splitting-based decode-and-forward relay in the presence of a mobile passive eavesdropper. Based on the Gamma-distributed first term of the Laguerre series, new statistical probability density function (PDF) and cumulative distribution function (CDF) expressions for the DN are derived to accurately model the complex cascaded fading scenario. The secrecy performance metrics analyzed are the secrecy outage probability (SOP), the probability of non-zero secrecy capacity (PNZSC), and the intercept probability (IP). In addition, the asymptotic SOP (ASOP) is investigated in the high signal-to-noise ratio (SNR) to enhance the comprehension of the secrecy performance. Based on the derived ASOP, the secrecy diversity order (SDO) of the proposed system is determined and examined. Particularly, we present analytical closed-form expressions for the secrecy performance metrics and provide a detailed understanding of the impact of the system parameters under the cascade fading scenario. Then, a power splitting (PS) optimization problem is formulated to minimize the SOP. The results demonstrate a reduction in the SOP with the proposed PS scheme compared to the equal PS scheme. The obtained analytical findings are validated using Monte Carlo simulations.

Profile constraint in toroidal plasmas and methodologies to break leading to transport barrier

Internal transport barriers (ITBs) observed in magnetically confined toroidal plasmas are promising for achieving high-performance burning plasmas, which are established from low-confinement L-mode plasmas dominated by anomalous transport exhibiting strong profile constraints. We studied the origin causing such L-mode plasmas using flux-driven gyro-kinetic based global toroidal simulations covering from core to edge. The simulations are incorporated with real space based statistical probability density function (PDF) approach, which directly measures the heat flux eddy distribution across the entire torus to identify the non-diffusive nature of turbulent transport with different spatio-temporal scales, such as micro-scale avalanches, macro-scale bursts, meso-scale E × B shear layers, etc., as the origin causing the constraints. Based on studies of such L-mode plasmas, we present a methodology to overcome such constraints and demonstrate ITB formations by the control of quasi-stationary global radial E × B shear through the toroidal plasma rotation driven by either externally using momentum injection and intrinsically using both ions and electron simultaneous heating.

A new description of probability density distributions of polar mesospheric clouds

Abstract. In this paper we present a new description of statistical probability density functions (pdfs) of polar mesospheric clouds (PMCs). The analysis is based on observations of maximum backscatter, ice mass density, ice particle radius, and number density of ice particles measured by the ALOMAR Rayleigh–Mie–Raman lidar for all PMC seasons from 2002 to 2016. From this data set we derive a new class of pdfs that describe the statistics of PMC events that is different from previous statistical methods using the approach of an exponential distribution commonly named the g distribution. The new analysis describes successfully the probability distributions of ALOMAR lidar data. It turns out that the former g-function description is a special case of our new approach. In general the new statistical function can be applied to many kinds of different PMC parameters, e.g., maximum backscatter, integrated backscatter, ice mass density, ice water content, ice particle radius, ice particle number density, or albedo measured by satellites. As a main advantage the new method allows us to connect different observational PMC distributions of lidar and satellite data, and also to compare with distributions from ice model studies. In particular, the statistical distributions of different ice parameters can be compared with each other on the basis of a common assessment that facilitates, for example, trend analysis of PMC.

A Newborn Track Detection and State Estimation Algorithm Using Bernoulli Random Finite Sets

In multi-target tracking (MTT) problems, there are many important issues that affect performance, including statistical filtering, measurement-target association, and estimating the number of targets. While newborn target detection and state estimation should also be considered as important factors in MTT, only a few studies have addressed these topics. In this paper, a novel newborn track detection and state estimation method is proposed using the concept of Bernoulli random finite sets. The posterior finite set statistical probability density function (FISST PDF) of a newborn target is analytically derived, and a tractable implementation scheme is proposed using importance sampling. Finally, the validity of the proposed method is demonstrated via integration with a Gaussian mixture probability hypothesis density (GM-PHD) filter and subsequent application to MTT problems.

Medium Access Probability of Cognitive Radio Network at 1900 MHz and 2100 MHz

Conventionally fading analysis of wireless LAN or MAN means small scale fading i.e. wide fluctuation of received signal with small variation of time and distance. In analysis of fading channel we consider the received signal in power, voltage or SNR as a random variable then statistical probability density function (pdf) like Rayleigh, Rician or Nakagami-m is used to get the probability of different phenomena. Most of the pdf is governed by two parameters: mean and variance of the random variable. In recent literature the mean value is taken constant but in this paper we consider the mean value as a slowly varying random variable and depend on the parameters of large scale fading. In this paper the concept of large and small scale fading is combined, in analysis of performance of cognitive radio network in context of medium access probability specially at 1900MHz and 2100MHz.

An Adaptive Tracking Algorithm Based on Mean Shift

Object tracking is to search the most similar parts to targets in video sequences. Among the various tracking algorithms, mean shift tracking algorithm has become popular due to its simplicity, efficiency and good performance. This paper focused on mean shift tracking algorithm, which is a modeling mechanism based on statistical probability density function. In practice, when the background of the tracking and characteristics of the target are similar, pixels of background occupy a large proportion in the histogram. The traditional mean shift cannot adapt to the mutative scene. Meanwhile, if there is block or disappearance, the result is not exact. Three algorithms were given for above difficulties. A weighted template background was established, that can highlight the features of target and improve real-time. Then this paper presented a selective mechanism to update the target model. Every component is updated based on the contribution to the target model. Finally, the Kalman filter was combined with mean shift algorithm. We saw the prediction points of Kalman filter as the initial point, carried out the mean shift iteration and then updated Kalman filter using the ultimate location. Extensive experimental results illustrated excellent agreement with these methods.

Comparing normal, lognormal and Weibull distributions for fitting diameter data from Akashmoni plantations in the north-eastern region of Bangladesh

Statistical probability density functions are widely used to model tree diameter distributions and to describe stand structure. The objective of this study was to compare the performance of normal, logarithmic-normal and three-parameter Weibull distributions for fitting diameter data from Akashmoni (Acacia auriculiformis A. Cunn. ex Benth.) plantations grown in the north-eastern region of Bangladesh. Data from 96 plots, established in 24 plantations in north-eastern Bangladesh and ranging in age from 1 to 6 years, were used for this study. The parameters of the Weibull distribution were calculated using maximum likelihood estimation (MLE) and moment estimation (ME) methods. The goodness of fit of normal, lognormal, Weibull MLE and Weibull ME were tested using one-sample Kolmogorov-Smirnov (KS) tests. The KS test results showed that both lognormal and Weibull distributions were equally effective for describing the diameter distributions of these Akashmoni plantations grown in the north-eastern region of Bangladesh.

RADIATION PATTERN SYNTHESIS FOR MAXIMUM MEAN EFFECTIVE GAIN WITH SPHERICAL WAVE EXPANSIONS AND PARTICLE SWARM TECHNIQUES

A new Mean Efiective Gain (MEG) expression using Spherical Wave Expansions (SWE) is presented in order to evaluate the impact of mobile environments on radiating structures. The proposed approach takes into account the pattern polarization and transforms a continuous functional optimization problem into an approximate discrete formulation. It allows to synthesize e-cient antenna radiation patterns in terms of the Mean Efiective Gain when it is combined with modern heuristic optimization techniques. In addition, antenna performance limits are evaluated by means of certain bounds. These depend on the modal number which is required to describe accurately far flelds and depend ultimately on the antenna size. The method estimates the optimum patterns for two difierent wireless scenarios that are characterized by the statistical probability density functions of incoming waves and particularized in the case of Gaussian statistics. The numerical evaluation has been performed by means of the Particle Swarm Optimization (PSO) technique, which is slightly modifled to include a speciflc constrain and whose parameters have been computed previously by solving a canonical problem. Finally, representative results in outdoor and mixed wireless scenarios are discussed, pointing out some useful consequences in antenna design.

On the probability density function model for the transport of particles in anisotropic turbulent flow

The purposes of the paper are twofold: (i) to present a rational approach to the modeling of inertial particle transport in anisotropic turbulent flows and (ii) to show how the anisotropy of fluid turbulence timescales affects the particle fluctuating velocities in homogeneous shear flow. For these purposes, the directional dependence of the Lagrangian autocorrelations of fluid velocities is incorporated into the statistical probability density function (PDF) model proposed previously. The anisotropic timescale (ATS) model is evaluated against numerical simulations for homogeneous shear turbulent flows and is compared to results predicted by the isotropic timescale (ITS) model. The new ATS model for the PDF of the particle velocity distribution in turbulent flow appears to yield slightly improved results over the ITS model.

Statistical Characterization of Particulate Properties of Some Industrial Powders

In this investigation, the statistical optic characterization approach is covered for four industrial powders, namely; gelatin, iron, tin and sodium chloride. For all of these powders few size fractions from sieve analysis are optically analyzed and the particles shape and size distributions are obtained. A discussion of the effect of these primary properties statistical distributions on some of the physical parameters (i.e. the secondary properties) including friction, flow and density is presented. A standard sample size determination technique for proper number of experimental data (i.e. particles) to obtain reliable and accurate results is utilized. Several standard statistical probability density function are attempted in order to obtain the best fit of the experimental statistical diameter histograms of particles. The Gamma probability function is found to be a suitable statistical model to fit the experimental particle diameter histograms of the four powders. Finally, a non-linear correlation is displayed between the fitted distribution function parameters and the measured secondary powder parameters.

Functional representation of a non-Markovian probability distribution in statistical mechanics

A path-integral representation of the statistical probability density function for a generalized non-linear and non-markovian Langevin equation is obtained.