Probability Distribution Law Research Articles

EVALUATION NOISE IMMUNITY OF THE BINARY DIGITAL MODEM WITH SIGNALS TYPE NOISE USING THE CHARACTERISTIC FUNCTION METHOD

The issue of improving modems with noise signals implies increasing the accuracy of theoretical estimation of noise immunity of the proposed methods of demodulation of information components of signals. Important is the task of assessing the immunity of digital modems, enabling engineers to ascertain the prospect of system development at the design stage. The article investigates the noise immunity of a binary digital modem with phase manipulation of the noise signal and the autocorrelation algorithm of its reception, which uses as noise carrier Gaussian signals. The paper presents a technique for calculating the bit error rate (BER) in a demodulator, which is characterized by the fact that the functional for estimating the received information bit contains components with different laws of probability distribution. The presented methodology is based on a mathematical apparatus of characte­ristic functions, which allows determining the potential noise immunity of a digital modem, providing a reduction of the discrepancies between theoretical and experimental data for determining the BER. Summing up the whole research it is worth noting the following research results: 1 noise immunity analysis of digital binary modem of noise signals was performed using mathematical apparatus of characteristic functions at autocorrelation method of operation of Gaussian type noise signal demodulator in the presence of Gaussian additive interference; 2 an analytical expression was found to calculate the characteristic density function of the random variable distribution at the output of a binary digital correlator; 3 the ratio was obtained to determine the potential noise immunity of the demodulator. The results of the study showed that the application of this technique eli­minates significant differences between the results of the theoretical evaluation of the noise immunity of the demodulator and the results of its simulation.

Delay-Distribution-Dependent H∞ State Estimation for Discrete-Time Memristive Neural Networks With Mixed Time-Delays and Fading Measurements.

This paper addresses the H ∞ state estimation issue for a sort of memristive neural networks in the discrete-time setting under randomly occurring mixed time-delays and fading measurements. The main purpose of the addressed issue is to propose a state estimator design algorithm that ensures the error dynamics of the state estimation to be stochastically stable with a prespecified H ∞ disturbance attenuation index. We put forward certain switching functions to account for the discrete-time yet state-dependent characteristics of the memristive connection weights. By resorting to the robust analysis theory and the Lyapunov-functional analysis theory, we derive some sufficient conditions to guarantee the desired estimation performance. The derived sufficient conditions rely not only on the size of discrete time-delays and the probability distribution law of the distributed time-delays but also on the statistics information of the coefficients of the adopted Rice fading model. Based on the established existence conditions, the gain matrices of the desired estimator are obtained by means of the feasibility of a set of matrix inequalities that can be checked efficiently via available software packages. Finally, the numerical simulation results are provided to show the validity of the main results.

ESPECIALLY THE MATHEMATICAL DESCRIPTION OF RANDOM SIGNALS WITH THREE LEVELS OF QUANTIZATION

The article describes the method of mathematical description of an additive mixture signal with noise when using the three‑level quantization. Method is based on the presentation of the implementation of the signal after quantization in the form of a random discrete 3D vector. It is proposed that statistical calculation technique characteristics of three‑level signals. The technique allows visualizing the probability distribution law of radar signals of different shapes on the background noise and calculating its numeric parameters. Knowledge of the law of probability distributions, assuming that the only inlet noise and distribution law of probability signal with noise allows to calculate the detection quality indicators to build a detector performance. Three‑level quantization allows to considerably simplify the technical implementation of electronic signal processing device with acceptable energy loss.

Prediction bands for solar energy: New short-term time series forecasting techniques

Short-term forecasts and risk management for photovoltaic energy is studied via a new standpoint on time series: a result published by P. Cartier and Y. Perrin in 1995 permits, without any probabilistic and/or statistical assumption, an additive decomposition of a time series into its mean, or trend, and quick fluctuations around it. The forecasts are achieved by applying quite new estimation techniques and some extrapolation procedures where the classic concept of “seasonalities” is fundamental. The quick fluctuations allow to define easily prediction bands around the mean. Several convincing computer simulations via real data, where the Gaussian probability distribution law is not satisfied, are provided and discussed. The concrete implementation of our setting needs neither tedious machine learning nor large historical data, contrarily to many other viewpoints.

Modelling procedures for assessing the effectiveness of innovative projects under the conditions of risk and uncertainty

While considering the current state of innovative projects, it is expedient to take into account the risk factor which makes it possible to adapt to the market environment. Due to high risks ways should be sought to minimize them. The research paper presents such methods of minimizing risks, namely: risk-sharing between project participants; carrying out insurance of projects; reserving funds for contingent expenses. With regard to characteristics of particular industry, the scheme for classification of innovative risks is proposed. It is pointed out that the distinguishing feature of innovation risks is that they are determined for each stage of the product innovation life cycle from the perspective of scientific, technological and commercial success. And then, the integral or, in other words, overall risk is determined. It is noted that in order to adequately assess the effectiveness of the project, it is necessary to have sufficient information to form a reasonable hypotheses about the probable distribution of the key parameters of the project. In such cases, the missing data is replaced by the values obtained in the process of determining the integral risk. The identification of integral risks is especially effective in cases where the processes under consideration are too complex, have a random (stochastic) nature or cannot be studied under real conditions. The simplest integral models are often used to generate source data that has some permissible properties. It is argued that in order to obtain the most accurate results it is expedient to use the method of problem-thematic (innovative) forecasting, since it will make it possible to take full account of all interconnections between the initial indicators of the project. The proposed procedures for assessing the effectiveness and risk management can be used by industrial enterprises that carry out risk management in order to avoid a crisis in an uncertain market environment. It is proved that in order to perform the procedures for assessing the effectiveness of innovative projects, it is necessary to follow five stages: to establish the relationships between initial and base indicators in the form of a mathematical equation or inequality; to set laws of probability distribution for key parameters of the model; to carry out computer simulation of knowledge of the key parameters of the model; to calculate the basic characteristics of probability distribution of initial and output indicators; to analyze the results and make decisions.

МЕТОД ГЕНЕРИРОВАНИЯ ДВУМЕРНОГО БИНАРНОГО СЛУЧАЙНОГО ПРОЦЕССА

The PURPOSE of the study is search for new and modernization of known generation methods of random processes with specified static (probability distribution law) and dynamic (correlation function) probabilistic properties. METHODS. The main research methods used in the study are the probability theory, mathematical statistics and numerical methods. RESULTS. The object of the study is a permutational technology of random process generation with a simultaneously specified probability distribution law and an autocorrelation function. This technology is simple in software implementation, has high response speed and allows to introduce the required probability properties with the accuracy of their reflection, sufficient for engineering applications (e.g. in simulation modeling). The Bernoulli (binary) law is taken as a law of probability distribution of the generated process. The conducted analysis of the probabilistic properties of the behavior of the permutation procedure components has resulted in the identification of new, previously unknown functional capabilities of this method of random process generation. Probabilistic properties (probability distribution laws and autocorrelation functions of the candidate vector components) are systematized depending on a mathematically justified permutation variant. The study is given to two variants of the permutational method that allows to generate a periodically correlated binary process. It is proved that these variants simultaneously provide the possibility to generate a two-dimensional binary random process. CONCLUSION. Conducted theoretical studies allowed to expand the functionalities of the permutational procedure of binary random process generation due to the possibility to generate a two-dimensional random binary process.

Effect of Zn Substitution on Magnetic Properties of CuFe2O4: a High-Temperature Series Expansions Study

The magnetic properties of spinel ferrites Cu1−xZnxFe2O4 are studied using high-temperature series expansions combined with the Padé approximates. The exchange interactions, inter and intra-sublattices , and are obtained using a probability distribution law. The critical exponent γ associated with the magnetic susceptibility is obtained.

Алгоритм определения законов распределения вероятностей параметров режимов и электрических величин при повреждениях в электрических сетях энергосистем

While considering certain problems in the electric power industry, the considered parameters, i.e. Steady State Mode and Fault Condition Parameters, operating values, etc. are the functional dependents of many arguments. Establishing the full probabilistic characteristics shall work to build up the understanding of all possible states, in which an object can exist. The challenge of their obtaining lies in the complexity of accounting for all the relationships between the random initial data when solving classical statistical methods, which does not have a full solution. The article presents the algorithms developed to apply the selection of interval boundaries of input and output data method to determine the probability distribution law for steady state mode and fault condition parameters of electric power system. A peculiar feature of these algorithms is the use of a universal total of random initial data consisting of quantiles of discrete orders. Thus, the number of universe general total variants can be substantially reduced, but the accuracy of the probabilistic characteristics formation is unchanged. The tasks were solved using the probability theory statement and mathematical statistics particularly in power engineering, numerical optimization methods. Also, MATLAB software package was used to solve the technical calculation problems. Determining the probabilistic characteristics of electrical dependencies in nondeterminate form allows executing the calculations practice in the electric power industry and electrical engineering, when the results are full and guaranteed, which allows for objective and reliable optimization and the precision of risks and accident event assessment. Software algorithms implementation solve a number of practical tasks, such as determining the probability laws for the risks of overload, emergency loss, and destruction.

Reliable Design: Basic Approach

The knowledge and experience learnt from product designing have resulted in development of their reliability theory. The classical concept of safe – life is based on product over dimensioned design that considers safety factor or safety margin for measure. However, practical engineering has found this concept in a manner inconvenient as design fault-resistance to determine the ultimate condition and operating stress are random values. A way out is in the concept of stochastic approach to reliability design resulting from the defect-production probability distribution law. That concept allows product designing with predetermined reliability, such as in the example contained in this paper.

Багатокритеріальна оптимізація кодів Лабі на основі природних обчислень

In modern packet-switched telecommunications networks error correcting coding used at different levels of the Open Systems Interconnection model. At the physical and data link layers to correct and detect errors in packets commonly used classic code constructions with a fixed coding rate (for example, block codes). On the other hand, to restore the whole packets code expedient use codes without fixed encoding rate at the application level. This class of codes are Luby codes that can be used alone or be part of the cascade code constructions. The key feature of these codes is to use the special law of probability distribution in the coding process. Wherein optimization of this distribution according to different objectives depending on the specific application Luby codes can improve their effectiveness. These objectives are redundant, failure rate, probability of failure, computational complexity of coding (decoding). In practice, there is often the need to use Luby codes simultaneously satisfy several objectives. To solve this multi-objective optimization problem an approach based on generalized procedures of natural computing is proposed. The main stages of the proposed approach are presented.

Homogeneity investigation of oil flax processing products by quality indexes

The paper analyzes the homogeneity of the stochastic structure of the samples of oil flax fibres of the Ukrainian and Polish selections. The distribution laws of fibres as mixtures of the normal and logarithmically normal distribution laws are identified. The general probability distribution law of fibre lengths of oil flax of the Ukrainian selection is a mixture of four logarithmically normal laws of distribution, and the general probability distribution law of fibre lengths of oil flax of the Polish selection is a mixture of a normal distribution law and three logarithmically normal laws of distribution. The parameters of the relevant components of the common distribution laws are found as a result of solving the problem of nonlinear optimization using the method of generalized lowering gradient that is implemented in Excel tabular processor. The adequacy of the built nonlinear models of the distribution laws is proved by estimating the value of the determination index. The comparative analysis of distribution laws of general totalities, from which the oil flax fibre samples of the Ukrainian and Polish selections are obtained, is conducted by the Kolmogorov-Smirnov statistical criterion. This criterion allows us to test and reject the hypothesis about belonging of two independent samples to the same general totality. The analysis of the general distribution laws shows that the oil flax fibres of the Ukrainian selection have a more pronounced tendency to stratification by a fibre length. Such a fibre is easily divided into factions. The oil flax fibres of the Polish selection have a larger part of short and extra-long fibres. Thus, it is clear that raw materials of the Ukrainian selection are more suitable for the production of non-woven materials of different target purposes, and the Polish selection - for the production of ropes, cords, etc. The obtained results can be used by specialists at processing enterprises for a reasonable choice of raw materials, optimization of processing modes and improving ready-made product quality.

Using Geometric and Exponential Distributions for the Prediction of Drift Parameters in Technical Objects

We develop a technique for stochastic prediction of the drift duration of technical parameters of objects within tolerances, using geometric and exponential probability distribution laws. We consider the application of this methodology when estimating the duration of the calibration interval of platinum resistance thermometers.

Goodness-of-fit tests for uniformity of probability distribution law

This paper describes a set of tests for uniformity of observations which are ranked by power. It is shown that most tests commonly used for the hypothesis of uniformity are biased relative to a certain kind of competing hypotheses. It is emphasized that specific tests meant only for uniformity have no obvious advantages over nonparametric goodness-of-fit tests used for the same purpose.

Systematic comparison of trip distribution laws and models

Trip distribution laws are basic for the travel demand characterization needed in transport and urban planning. Several approaches have been considered in the last years. One of them is the so-called gravity law, in which the number of trips is assumed to be related to the population at origin and destination and to decrease with the distance. The mathematical expression of this law resembles Newton's law of gravity, which explains its name. Another popular approach is inspired by the theory of intervening opportunities which argues that the distance has no effect on the destination choice, playing only the role of a surrogate for the number of intervening opportunities between them. In this paper, we perform a thorough comparison between these two approaches in their ability at estimating commuting flows by testing them against empirical trip data at different scales and coming from different countries. Different versions of the gravity and the intervening opportunities laws, including the recently proposed radiation law, are used to estimate the probability that an individual has to commute from one unit to another, called trip distribution law. Based on these probability distribution laws, the commuting networks are simulated with different trip distribution models. We show that the gravity law performs better than the intervening opportunities laws to estimate the commuting flows, to preserve the structure of the network and to fit the commuting distance distribution although it fails at predicting commuting flows at large distances. Finally, we show that the different approaches can be used in the absence of detailed data for calibration since their only parameter depends only on the scale of the geographic unit.

Probabilistic Model of Technical Queuing Systems with Subsystems for Detection and Recovery of Failures

The given article presents an analytical model developed for a multichannel technical queuing system with time redundancy for operability management, subsystems of reliable periodical control of sudden and gradual failure detection and a subsystem for system recovery after failure. It is assumed in the model that the failures are governed by the Poisson probability distribution law and the times of reliable control and system recovery after failures are governed by an arbitrary law of probability distribution, in the general case depending on the number of servicers. The paper defines probabilities of accomplishment of certain task volumes by the system within a priori defined time intervals, taking into consideration its reliability characteristics.

О КРИТЕРИЯХ ПРОВЕРКИ РАВНОМЕРНОСТИ ЗАКОНА РАСПРЕДЕЛЕНИЯ ВЕРОЯТНОСТЕЙ

О КРИТЕРИЯХ ПРОВЕРКИ РАВНОМЕРНОСТИ ЗАКОНА РАСПРЕДЕЛЕНИЯ ВЕРОЯТНОСТЕЙ

Еstimation of intrusion detection probability by passive infrared detectors

Subject of Research. The paper deals with estimation of detection probability of intruder by passive infrared detector in different conditions of velocity and direction for automated analyses of physical protection systems effectiveness. Method. Analytic formulas for detection distance distribution laws obtained by means of experimental histogram approximation are used. Main Results. Applicability of different distribution laws has been studied, such as Rayleigh, Gauss, Gamma, Maxwell and Weibull distribution. Based on walk tests results, approximation of experimental histograms of detection distance probability distribution laws by passive infrared detectors was done. Conformity of the histograms to the mentioned analytical laws according to fitting criterion 2 has been checked for different conditions of velocity and direction of intruder movement. Mean and variance of approximate distribution laws were equal to the same parameters of experimental histograms for corresponding intruder movement parameters. Approximation accuracy evaluation for above mentioned laws was done with significance level of 0.05. According to fitting criterion 2, the Rayleigh and Gamma laws are corresponded mostly close to the histograms for different velocity and direction of intruder movement. Dependences of approximation accuracy for different conditions of intrusion have been got. They are usable for choosing an approximation law in the certain condition. Practical Relevance. Analytic formulas for detection probability are usable for modeling of intrusion process and objective effectiveness estimation of physical protection systems by both developers and users.

The simulation of occasional road disturbances for studying mobile vehicles dynamics

This paper presents a procedure for simulating random road disturbances based on the method of non-canonically decomposing random functions in the form of deterministic functions depending on just three random quantities under any probability distribution law. The mathematical methods developed for modeling random road disturbances give an accurate representation of the random function perturbations in the framework of the correlation theory using just three random variables. The proposed approach allows to obtain more reliable data on the spectral composition of the microrelief, to simplify the study of the dynamics of mobile vehicles and reduce the amount of computation in comparison with other methods.

MODELING AND OPTIMIZATION OF PARALLEL INFORMATION SEARCHING IN FILES

In this article the m-parallel method of sequential field searching and two variants of m-parallel block field searching method are offered. These methods are oriented to be used in multiprocessing system for information searching in files of database. We research the effectiveness of these methods for different probability distribution law of field access. The mathematical expectation of number of parallel comparisons necessary for field searching in files is taken as a criterion of effectiveness. The effectiveness of the methods is compared and analyzed. The best of offered methods is founded for every considered probability distribution. Optimal strategies of field searching in sequenced files stored in external memory of multiprocessing system are made. In this case the mathematical expectation of total time needed for field searching in files is taken as a criterion of effectiveness.

Magnetic properties of mixed Ni–Cu ferrites calculated using mean field approach

The magnetic properties of spinel ferrites [Fe1−(1−x)y3+Cu(1−x)y2+]A[Nix2+Cu(1−x)(1−y)2+Fe1+(1−x)y3+]BO4 have been studied by the mean field theory (MFT) and high temperature series expansions (HTSEs) combined with the Padé approximants. The critical temperature, the saturation magnetisation (MS) and the intra-sublattice exchanges interactions (JAA(x,y), JBB(x,y) and JAB(x,y)) are obtained by using a probability distribution law. The critical exponents associate with the magnetic susceptibility have been obtained. The effect of copper doping on the magnetic properties of nickel ferrites has been examined.