An explicit formula relating the probability density function with its cumulants is derived and discussed. A generalization of the Gram-Charlier expansion is presented, allowing to express one PDF in terms of another. The coefficients of this general expansion are explicitly obtained.

This paper incorporates robustness into neural network modeling and proposes a novel two-phase robustness analysis approach for determining the optimal feedforward neural network (FNN) architecture in terms of Hellinger distance of probability density function (PDF) of error distribution. The proposed approach is illustrated with an example in this paper.

A natural way to estimate the probability density function of an unknown distribution from the sample of data points is to use histograms. The accuracy of the estimate depends on the size of the histogram’s bins. There exist heuristic rules for selecting the bin size. In this paper, we show that these rules indeed provide the optimal value of the bin size. 1 Formulation of the Problem Need to e...

This contribution proposes a novel probability density function (PDF) estimation based over-sampling (PDFOS) approach for two-class imbalanced classification problems. The classical Parzen-window kernel function is adopted to estimate the PDF of the positive class. Then according to the estimated PDF, synthetic instances are generated as the additional training data. The essential concept is to...

—A frequent problem in digital communications is the computation of the probability density function (pdf) and cumulative distribution function (cdf), given the characteristic function (chf) of a random variable (RV). This problem arises in signal detection , equalizer performance, equal-gain diversity combining, in-tersymbol interference, and elsewhere. Often, it is impossible to analytically ...

We present an experimental study on the local dynamics of parametrically excited waves at an air–water interface when defects are present in the wave pattern. The probability density function (PDF) of the local wave amplitude displays an exponential part for values close to the average amplitude and decreases sharply to zero for large amplitudes. The power spectral density (PSD) of the local am...

We show that the results obtained through clusteringbased image segmentation of single or multi-component images can be improved by a fuzzy relaxation of the degrees of membership in the image space. We illustrate the point through two clustering techniques: the fuzzy Cmeans (FCM) technique and a clustering technique based on the estimation of the probability density function (pdf).

1.0 Rayleigh Distribution Using central limit theorem arguments, one can show that the I and Q channels on a mobile radio multipath fading channel are independent Gaussian (normal) random variables. Jakes [1] and others show that the envelope of two independent and identically distributed (iid) Gaussian random variables is Rayleigh distributed.1 Probability Density Function (pdf) (usual form fo...

We propose the exact calculation of the probability density function (PDF) and cumulative distribution function (CDF) of mutual information (MI) for a two-user MIMO MAC network over block Rayleigh fading channels. So far the PDF and CDF have been numerically evaluated since MI depends on the quotient of two Wishart matrices, and no closed-form for this quotient was available. We derive exact re...

In this paper, a performance analysis of amplifyand-forward (AF) relaying cooperative diversity system with relay selection is given when all terminals are moving. We have derived analytical expressions for probability density function (PDF), cumulative distribution function (CDF) and moment generating function (MGF) of end-to-end signal-to-noise ratio (SNR) for the considered system. Then, the...