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...

This article derives the probability density function (pdf) of the sum of a normal random variable and a (sphered) Student’s-t distribution on odd degrees of freedom greater than or equal to three. Apart from its intrinsic interest applications of this result include Bayesian wavelet shrinkage, Bayesian posterior density derivations, calculations in the theoretical analysis of projection indice...

A parametric method similar to autoregressive spectral estimators is proposed to determine the probability density function (pdf) of a random set. The method proceeds by maximizing the likelihood of the pdf, yielding estimates that perform equally well in the tails as in the bulk of the distribution. It is therefore well suited for the analysis short sets drawn from smooth pdfs and stands out b...

A novel asymptotic closed-form probability density function (pdf) of the two-hop (TH) link is derived for a simultaneous wireless information and power transfer based differential amplify-andforward system. Based on the pdf, asymptotic closed-form average bit-error rate expressions of the single TH link and the TH link with direct link combined with a linear combining scheme are both derived. M...

In this paper, we present a noisy version of the algebraic geometric approach of identifying parameters of discrete-time linear hybrid system. Two approximate ways of estimating hybrid parameters are considered: one is using MSE criteria, while the other is based on the information divergence that measures the distance between the error probability density function (PDF) of the identified model...

this paper, a new probability density function (pdf) is proposed to model the statistics of wavelet coefficients, and a simple Kalman's filter is derived from the new pdf using Bayesian estimation theory. Specifically, we decompose the speckled image into wavelet subbands, we apply the Kalman's filter to the high subbands, and reconstruct a despeckled image from the modified detail coefficients...

this paper presents a probabilistic optimal power flow (popf) algorithm considering different uncertainties in a smart grid. different uncertainties such as variation of nodal load, change in system configuration, measuring errors, forecasting errors, and etc. can be considered in the proposed algorithm. by increasing the penetration of the renewable energies in power systems, it is more essent...

Weak lensing measurements are starting to provide statistical maps of the distribution of matter in the universe that are increasingly precise and complementary to cosmic microwave background maps. The probability distribution (PDF) provides a powerful tool to test non-Gausian features in the convergence field and to discriminate the different cosmological models. In this letter, we present a n...

The outage probability of the Switch and Stay Combining/Selection Combining (SSC/SC) combiner output signal at two time instants, in the presence of log-normal fading, is determined in this paper. The probability density function (PDF) of the combiner output signal is derived. Then, the outage probability is numerically calculated using this PDF. The results are shown graphically to compare per...

Abstract: Closed form expressions for the PDF and MGF of the harmonic mean of two independent exponential variates are cited and derived, and then applied to study the performance of cellular multi-node and dual-hop cooperative communication systems with non-regenerative relays over flat Rayleigh fading channels. We derive the probability density function (PDF) and asymptotic symbol error rate ...