The impact of the third (skewness) and fourth (kurtosis) reduced centered moments on the statistical modeling of E1 lines in complex atomic spectra is investigated through the use of Gram-Charlier, Normal Inverse Gaussian and Generalized Gaussian distributions. It is shown that the modeling of unresolved transition arrays with nonGaussian distributions may reveal more detailed structures, due e...

The global maximum of an entropy function with different decision levels for a three-level scalar quantizer performed after a discrete wavelet transform was derived. Herein, we considered the case of entropy-constrained scalar quantization capable of avoiding many compression ratio reductions as the mean squared error was minimized. We also dealt with the problem of minimum entropy with an erro...

In this paper, we propose a methodology for training a new model of artificial neural network called the generalized radial basis function (GRBF) neural network. This model is based on generalized Gaussian distribution, which parametrizes the Gaussian distribution by adding a new parameter t. The generalized radial basis function allows different radial basis functions to be represented by upda...

We show that the generating functions of the generalized Catalan numbers can be identified with the moment generating functions of probability density functions related to the Brownian motion stochastic process. Specifically, the probability density functions are exponential mixtures of inverse Gaussian (EMIG) probability density functions, which arise as the first passage time distributions to...

In this paper, we present an algorithm for the problem of multi-channel blind deconvolution which can adapt to unknown sources with both sub-Gaussian and super-Gaussian probability density distributions using a generalized exponential source model. We use a state space representation to model the mixer and demixer respectively, and show how the parameters of the demixer can be adapted using a g...

For the first time, an explicit closed form expression is derived for the characteristic function of the generalized normal distribution (GND). Also derived is an expression for the correlation coefficient between variate-values and their ranks in samples from the GND. The expression for the former involves the Fox-Wright generalized confluent hypergeometric 1Ψ0-function, while the latter is ex...

in this paper, a bayesian approach is proposed for shift point detection in an inverse gaussian distribution. in this study, the mean parameter of inverse gaussian distribution is assumed to be constant and shift points in shape parameter is considered. first the posterior distribution of shape parameter is obtained. then the bayes estimators are derived under a class of priors and using variou...

The Kramers’ theory of activated processes is generalized for nonequilibrium open systems. We consider both the internal noise due to thermal bath and the external noise which are stationary, Gaussian and are characterized by arbitrary decaying correlation functions. We stress the role of a nonequilibrium stationary state distribution for this open system which is reminiscent of an equilibrium ...

This paper handles the problem of detecting signals with known form and structure and unknown or random amplitude and phase in the presence of compound-Gaussian noise with known spectral density in remote sensing systems. The generalized detector (GA) based on the generalized approach to signal processing (GASP) in noise is investigated in [1]–[5]. The structure of the GA detector is independen...

In this paper, we present a generalized accurate methodology to predict the bit error rate performance for non-coherent chaos-based communication systems. The Gaussian approximation approach, which is widely used to compute the performance of such systems, leads to inaccurate results, especially with respect to low spreading factors. Our new approach based on the chaos bit energy distribution g...