The uniformly minimum variance unbiased (UMVU), maximum likelihood, percentile (PC), least squares (LS) and weighted least squares (WLS) estimators of the probability density function (pdf) and cumulative distribution function are derived for the generalized Rayleigh distribution. This model can be used quite effectively in modelling strength data and also modeling general lifetime data. It has...

We continue to explore the hypothesis that neuronal populations represent and process analog variables in terms of probability density functions (PDFs). A neural assembly encoding the joint probability density over relevant analog variables can in principle answer any meaningful question about these variables by implementing the Bayesian rules of inference. Aided by an intermediate representati...

We show how disordered media allow to increase the local degree of polarization (DOP) of an arbitrary (partial) polarized incident beam. The role of cross-scattering coefficients is emphasized, together with the probability density functions (PDF) of the scattering DOP. The average DOP of scattering is calculated versus the incident illumination DOP.

Distance or similarity measures are essential to solve many pattern recognition problems such as classification, clustering, and retrieval problems. Various distance/similarity measures that are applicable to compare two probability density functions, pdf in short, are reviewed and categorized in both syntactic and semantic relationships. A correlation coefficient and a hierarchical clustering ...

Various existing criteria to characterize the statistical independence are applied in blind source separation and independent component analysis. However, almost all of them are based on parametric models. The distribution model mismatch between the output PDF (Probability Density Functions) and the chosen underlying distribution model is a serious problem in blind signal processing. Non-parame...

This paper proposes the use of Gaussian Mixture Models to estimate conditional probability density functions in an environmental risk mapping context. A conditional Gaussian Mixture Model has been compared to the geostatistical method of Sequential Gaussian Simulations and shows good performances in reconstructing local PDF. The data sets used for this comparison are parts of the digital elevat...

The adaptive rejection sampling (ARS) algorithm is a universal random generator for drawing samples efficiently from a univariate log-concave target probability density function (pdf). ARS generates independent samples from the target via rejection sampling with high acceptance rates. Indeed, ARS yields a sequence of proposal functions that converge toward the target pdf, so that the probabilit...

We determine that the sizes of bursts in current density in an RMHD simulation follow power-law probability density functions (PDF). The PDFs of duration and waiting time between bursts also resemble power laws, and are clearly not exponential. This suffices to distinguish their behaviour from the original Bak et al. sandpile model which had exponential waiting time PDFs, but will not distingui...

We consider a sequence of independent and identicaly distributed (iid) random variables with absolutely continuous distribution function F(x) and probability density function (pdf) f(x). Let Rnl be the largest observation after observing nth record and R(ns) be the smallest observation after observing the nth record. Then we say Wnr = Rnl− R(ns), n > 1, as the nth record range. We will c...