Search results for "Probability density function"
showing 10 items of 183 documents
Introducing randomness in the analysis of chemical reactions: An analysis based on random differential equations and probability density functions
2021
[EN] In this work we consider a particular randomized kinetic model for reaction-deactivation of hydrogen peroxide decomposition. We apply the Random Variable Transformation technique to obtain the first probability density function of the solution stochastic process under general conditions. From the rst probability density function, we can obtain fundamental statistical information, such as the mean and the variance of the solution, at every instant time. The transformation considered in the application of the Random Variable Transformation technique is not unique. Then, the first probability density function can take different expressions, although essentially equivalent in terms of comp…
Solving fully randomized higher-order linear control differential equations: Application to study the dynamics of an oscillator
2021
[EN] In this work, we consider control problems represented by a linear differential equation assuming that all the coefficients are random variables and with an additive control that is a stochastic process. Specifically, we will work with controllable problems in which the initial condition and the final target are random variables. The probability density function of the solution and the control has been calculated. The theoretical results have been applied to study, from a probabilistic standpoint, a damped oscillator.
Path-wise versus kinetic modeling for equilibrating non-Langevin jump-type processes
2014
We discuss two independent methods of solution of a master equation whose biased jump transition rates account for long jumps of L\'{e}vy-stable type and nonetheless admit a Boltzmannian (thermal) equilibrium to arise in the large time asymptotics of a probability density function $\rho (x,t)$. Our main goal is to demonstrate a compatibility of a {\it direct} solution method (an explicit, albeit numerically assisted, integration of the master equation) with an {\it indirect} path-wise procedure, recently proposed in [Physica {\bf A 392}, 3485, (2013)] as a valid tool for a dynamical analysis of non-Langevin jump-type processes. The path-wise method heavily relies on an accumulation of large…
Information potential for some probability density functions
2021
Abstract This paper is related to the information theoretic learning methodology, whose goal is to quantify global scalar descriptors (e.g., entropy) of a given probability density function (PDF). In this context, the core concept is the information potential (IP) S [ s ] ( x ) : = ∫ R p s ( t , x ) d t , s > 0 of a PDF p(t, x) depending on a parameter x; it is naturally related to the Renyi and Tsallis entropies. We present several such PDF, viewed also as kernels of integral operators, for which a precise relation exists between S[2](x) and the variance Var[p(t, x)]. For these PDF we determine explicitly the IP and the Shannon entropy. As an application to Information Theoretic Learning w…
ESCAPE TIMES IN STOCK MARKETS
2005
We study the statistical properties of escape times for stock price returns in the Wall Street market. In particular we get the escape time distribution for real data from daily transactions and for three models: (i) the Wiener process with drift and a constant market volatility, (ii) Heston and (iii) GARCH models, where the volatility is a stochastic process. We find that the first model is unable to catch all the features of the escape time distribution of real data. Moreover, the Heston model describes the probability density function for both return and escape times better than the GARCH model.
Fatigue life under non-Gaussian random loading from various models
2004
Fatigue test results on the 10HNAP steel under constant amplitude and random loading with non-Gaussian probability distribution function, zero mean value and wide-band frequency spectrum have been used to compare the life time estimation of the models proposed by Bannantine, Fatemi–Socie, Socie, Wang–Brown, Morel and Łagoda–Macha. Except the Morel proposal which accumulates damage step by step with a proper ethodology, all the other models use a cycle counting method. The rainflow algorithm is used to extract cycles from random histories of damage parameters in time domain. In the last model, where a strain energy density parameter is employed, additionally spectral method is evaluated for …
Spectral analysis of the criteria for multiaxial Random Fatigue
1991
In the paper the spectral analysis of several fatigue criteria under simple and complex states of stress has been done and limitations appearing while formulating new criteria for multiaxial random loadings have been shown. The presented analysis includes determination, with digital simulation, of probability density function and power spectral density function of the equivalent stress according to three special linear criteria of multiaxial random fatigue and six nonlinear criteria. Calculations were carried out for four kinds of random stress state. It has been shown that mathematical models for the criteria of multiaxial random fatigue formulated as nonlinear combinations of stress state…
Exploring the uncertainty in capacity estimation at roundabouts
2017
Abstract Purpose In gap-acceptance theory the critical and the follow-up headways have a significant role in determining roundabout entry capacities which in turn depend on circulating flow rates under a specified arrival headway distribution. Calculation considers single mean values of the gap-acceptance parameters, neglecting the inherent variations in these random variables and providing a single value of entry capacity. The purpose of this paper is to derive the entry capacity distribution which accounts for the variations of the contributing (random) variables and suggest how to consider this issue in the operational analysis of the roundabouts. Methods We performed a Monte Carlo simul…
Geometry-Based Modeling of Wideband Industrial Indoor Radio Propagation Channels
2015
In this paper, we present a geometrical scattering model for a typical class of industrial indoor environments. The proposed industrial reference model takes into account scattering components arising from metallic structures and the surrounding walls of the investigated environment. Starting from the geometrical scattering model, we derive the analytical expressions of the probability density function (PDF) of the angle of arrival (AoA), PDF of the time of arrival (ToA), and the autocorrelation function (ACF) in the frequency domain. The obtained results reveal a large difference between industrial channels and other home and office environments. The theoretical results of the reference mo…
Generalized feed-forward based method for wind energy prediction
2013
Abstract Even though a number of new mathematical functions have been proposed for modeling wind speed probability density distributions, still the Weibull function continues to be the most commonly used model in the literature. Therefore, the parameters of this function are still widely used to obtain typical wind probability density distributions for finding the wind energy potential by researchers, engineers and designers. Once long-term average of Weibull function’s parameters are known, then the probability density distributions can easily be obtained. Artificial neural network (ANN) can be used as alternative to analytical approach as ANN offers advantages such as no required knowledg…