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.

A selection combining scheme for RAKE receivers

Abstract: A selection combining scheme for a RAKE receiver operating over a multipath fading channel is introduced, by which the m largest channel outputs are selected instead of only the largest one, as in the conventional selection combining receiver. Expressions for the error probability of this scheme for an exponential multipath intensity profile (MIP) with arbitrary decay constant are found by first deriving the joint density function of the m ordered channel outputs, then averaging the conditional error probability over the joint density function. The performance is compared with that of maximal ratio combining in both an interference-limited and a noise-limited environment. The interference-limited environment chosen is a multicell CDMA system. Numerical results show that the performance of the selection combining scheme is superior to that of conventional selection combining, and can be very close to that of maximal ratio combining, depending upon the value of m and the rate of decay of the MIP.

A new probabilistic power flow analysis method

Abstract: A method for the simulation of the composite power system is proposed for the purpose of evaluating the probability distribution function of circuit flows and bus voltage magnitudes. The method consists of two steps. First, given the probabilistic electric load model, the probability distribution function of the total generation of generation buses is computed. Second, circuit flows and bus voltage magnitudes are expressed as linear combinations of power injections at generation buses. This relationship allows the computation of the distribution functions of circuit flows and bus voltage magnitudes. The method incorporates major operating practices such as economic dispatch and nonlinearities resulting from the power flow equations. Validation of the method is performed via Monte Carlo simulation. Typical results are presented, showing that the proposed method matches the results obtained with the Monte Carlo simulations very well. Potential applications of the proposed method are: composite power system reliability analysis and transmission loss evaluation. >

Stationary states of non-linear oscillators driven by Lévy noise

Abstract: We study the probability density function in the stationary state of non-linear oscillators which are subject to Levy stable noise and confined within symmetric potentials of the general form U(x)∝x 2m+2 /(2m+2), m=0,1,2,… . For m⩾1, the probability density functions display a distinct bimodal character and have power-law tails which decay faster than those of the noise probability density. This is in contrast to the Levy harmonic oscillator m=0. For the particular case of an anharmonic Levy oscillator with U(x)=ax2/2+bx4/4, a>0, we find a turnover from unimodality to bimodality at stationarity.

Nonlinear filtering by approximation of the a posteriori density

Abstract: The problem of estimating from noisy measurement data the state of a dynamical system described by non-linear difference equations is considered. The measurement data have a non-linear relation with the state and are assumed to be available at discrete instants of time. A Bayesian approach to the problem is suggested in which the density function for the state conditioned upon the available measurement data is computed recursively. The evolution of the a posteriori density function cannot be described in a closed form for most systems; the class of linear systems with additive, white gaussian noise provides the major exception. Thus, the problem of non-linear filtering can be viewed as essentially a problem of approximating this density function. For linear systems with additive, white gaussian noise, the a posteriori density is gaussian. The results for linear systems are frequently applied to non-linear systems by introducing linear perturbation theory. Then, the linear equations and gaussian a posterio...

I–K distribution as a universal propagation model of laser beams in atmospheric turbulence

Abstract: A new propagation model is developed for the intensity fluctuations of a laser beam propagating through extended clear-air turbulence. The field of the optical wave is modeled as the sum of a coherent (deterministic) component and a random component, the intensity of which is assumed governed by the generalized n distribution of Nakagami. We further assume that the statistics are inherently nonstationary by treating the average intensity of the random portion of the field as a fluctuating quantity. The resulting unconditional I–K distribution for the intensity fluctuations is a generalized form of the K distribution that is applicable to all conditions of atmospheric turbulence for which data have been obtained, including weak turbulence for which the K distribution is not theoretically applicable.