In this paper, we propose an exact analytical technique to evaluate the average capacity of a dual-hop OFDM relay system with decode-and-forward protocol in an independent and identical distribution (i.i.d.) Rayleigh fading channel. Four schemes, (no) matching “and” or “or” (no) power allocation, will be considered. First, the probability density function (pdf) for the end-to-end power channel ...

A new distance measure between probability density functions (pdfs) is introduced, which we refer to as the Laplacian pdf distance. The Laplacian pdf distance exhibits a remarkable connection to Mercer kernel based learning theory via the Parzen window technique for density estimation. In a kernel feature space defined by the eigenspectrum of the Laplacian data matrix, this pdf distance is show...

We introduce and establish some properties of a generalized form of the beta function. Corresponding generalized incomplete beta functions are also defined. Moreover, we define a new probability density function (pdf) involving this new generalized beta function. Some basic functions associated with the pdf, such as moment generating function, mean residue function, and hazard rate function are...

This paper extends the use of stochastic watershed, recently introduced by Angulo and Jeulin [1], to unsupervised segmentation of multispectral images. Several probability density functions (pdf), derived from Monte Carlo simulations (M realizations of N rsandom markers), are used as a gradient for segmentation: a weighted marginal pdf a vectorial pdf and a probabilistic gradient. These gradien...

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. ...

From the integration of nonsymmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. Motivated by the mathematical curiosity, we show that these generalized functions are suitable to generalize some probability density functions pdfs . A very reliable rank distribution can be conveni...

The probability density function (PDF) of the surface electromyogram (EMG) signals has been modelled with Gaussian and Laplacian distribution functions. However, a general consensus upon the PDF of the EMG signals is yet to be reached, because not only are there several biological factors that can influence this distribution function, but also different analysis techniques can lead to contradic...

Concentrations of chemical species transported in random environments need to be statistically characterized by probability density functions (PDF). Solutions to evolution equations for the one-point one-time PDF are usually based on systems of computational particles described by Itô equations. We establish consistency conditions relating the concentration statistics to that of the Itô process...

We consider a wide class of spiking neuron models, defined by rather general set of conditions typical for basic models like leaky integrate and fire, or binding neuron model. A neuron is fed with a point renewal process. A relation between the three probability density functions (pdf): (i) pdf of input interspike intervals, (ii) pdf of output interspike intervals of a neuron with instantaneous...