We report that the power driving gravity and capillary wave turbulence in a statistically stationary regime displays fluctuations much stronger than its mean value. We show that its probability density function (PDF) has a most probable value close to zero and involves two asymmetric roughly exponential tails. We understand the qualitative features of the PDF using a simple Langevin-type model.

We obtain an expression for the probability density function (PDF) of partially developed speckles formed by light with an arbitrary degree of polarization. From the probability density we calculate the detection threshold corresponding to the 5σ confidence level of a normal distribution. We show that unpolarized light has an advantage in high contrast imaging for low ratios of the deterministi...

The mathematical methods required to model simple stochastic processes are reviewed briefly. These methods are used to determine the probability-density function (PDF) for noise-induced energy perturbations of isolated (solitary) optical pulses in fiber communication systems. The analytical formula is consistent with the numerical solution of the energymoment equation. System failures are cause...

We propose a new method for background modeling. Our method is based on the two complementary approaches. One uses the probability density function (PDF) to approximate background model. The PDF is estimated non-parametrically by using Parzen density estimation. Then, foreground object is detected based on the estimated PDF. The method is based on the evaluation of the local texture at pixel-le...

In this paper the Weibull fading channel model is described and some integral characteristics of Weibull distribution are analyzed. For analytical and numerical evaluation of system performance, the Weibull probability density functions (pdf) are analyzed like particular solutions of corresponding differential equation, while the existence of singular solution is considered and analyzed under d...

When a probability density function (pdf) is to be formed on the basis of incomplete information, the “maximum missing information” (mmi) pdf (Jaynes. Phys. Reo. 106, 62M30, 1957) is theoretically preferable. We compare the performance of Lagrangian stochastic (LS) models of vertical dispersion in the convective boundary layer. satisfying Thomson’s (J. Fluid Mech. 180,529-556, 1987) well-mixed ...

In this paper, a new method is proposed in order to evaluate the stochastic solution of linear random differential equation. The method is based on the combination of the probabilistic transformation method for a single random variable and the numerical methods (e.g. finite difference, finite element, Runge-Kutta, etc...). The transformation technique evaluates the probability density function ...

In this paper, a new blind equalization algorithm for multilevel modulations is proposed. It is based on maximizing the correlation between the probability density function (pdf) of the signal at the output of the equalizer and the desired pdf. The algorithm employs the Parzen window method to estimate the pdf of the squared modulus of the equalizer output. A stochastic gradient-based algorithm...

Robustness against outliers is a desirable property of any unsupervised learning scheme. In particular, probability density estimators benefit from incorporating this feature. A possible strategy to achieve this goal is to substitute the sample mean and the sample covariance matrix by more robust location and spread estimators. Here we use the L1-median to develop a nonparametric probability de...

The problem of determining the distances and their uncertainties from the measurements of parallaxes has no straight forward solution. In contrast to Bayesian-like approaches, a direct approach is possible assuming that the probability density function (pdf) in relative distance is cut for negative distances. This gives an asymmetrical pdf which is difficult to use and overestimates variances. ...