The probability distribution functions (PDF) of density of the interstellar medium (ISM) in galactic disks and global star formation rate are discussed. Three-dimensional hydrodynamic simulations show that the PDFs in globally stable, inhomogeneous ISM in galactic disks are well fitted by a single lognormal function over a wide density range. The dispersion of the log-normal PDF (LN-PDF) is lar...

This article derives the probability density function (pdf) of the sum of a normal random variable and a (sphered) Student’s-t distribution on three degrees of freedom. Advice is given on deriving the convolution density for higher degrees of freedom. Apart from its intrinsic interest applications of this result include Bayesian wavelet shrinkage, Bayesian posterior density derivations, calcula...

The article derives a novel Gram-Charlier A (GCA) Series based Extended Rule-of-Thumb (ExROT) for bandwidth selection in Kernel Density Estimation (KDE). There are existing various bandwidth selection rules achieving minimization of the Asymptotic Mean Integrated Square Error (AMISE) between the estimated probability density function (PDF) and the actual PDF. The rules differ in a way to estima...

This paper introduces a novel motion planning algorithm for stochastic scenarios. We extend the concept of a navigation function to such scenarios. Our main idea is to consider both the Gaussian distribution probabilities of the players’ locations and disc (or star sets) geometry of the objects operating in the work space. We do so by formulating a probability density function that encloses bot...

Review 2 Bayesian Classification For a given pattern x, classify it to the most probable class. 1 Probabilistic Classification Recall the problem with the MICD. The MICD always favours C 2. Instead, we ideally want it to favour the class with the highest probability: P (C i |x) C i ≷ C j P (C j |x) where P (C i |x) is the a posteriori (after measurement) probability of class C i given x. To get...

This paper addresses the problem of estimating the model parameters of a piecewise multi-linear (PML) approximation to a probability density function (PDF). In an earlier paper, we already introduced the PML model and discussed its use for the purpose of designing Bayesian pattern classifiers. The estimation of the unknown model parameters was based on a least squares minimisation of the differ...

We present an experimental study of turbulent convection in a cell with staggered fingers on its sidewall using water as the convecting fluid. Our measurements reveal that Nu , Ra20.27, and that the temperature probability density function (PDF) at the cell center is a double-peaked function which can be fitted by the superposition of two Gaussians. Moreover, it is found that the size of the lo...

This comment corrects several errors found in the paper, “Class of Cyclic-Based Estimators for Frequency-Offset Estimation of OFDM Systems.” In addition, we show that the minimum variance unbiased estimator for frequency offset derived in the above paper is the maximum-likelihood estimator when the timing delay is perfectly known. I. SYSTEM MODEL F irst, the probability density function (pdf) o...

In the context of digital signal processing addressed to underwater acoustic communications, this work focuses attention on the optimization of detection of weak signals in presence of additive independent stationary non-Gaussian noise. In order to detect signals in the case of low SNR values, the selected binary statistical testing approach consists in a Locally Optimum Detector (LOD), designe...

We report experimental results on the acceleration component probability distribution function at R λ = 690 to probabilities of less than 10 −7. This is an improvement of more than an order of magnitude over past measurements and allows us to conclude that the fourth moment converges and the flatness is approximately 55. We compare our probability distribution to those predicted by several mode...