Related papers: Probability density function and detection thresho…
Monochromatic light is prepared by a single slit of spatial width {\Delta}x. The diffraction pattern is considered to obtain the corresponding probability density of the momentum. Let P be the probability weight to measure a momentum in a…
Aims:Calibrating the point spread function (PSF) is a fundamental part of weak gravitational lensing analyses. Even with corrected galaxy images, imperfect calibrations can introduce biases. We propose an analytical framework for…
We measure the z=0 B-band optical luminosity function (LF) for galaxies selected in a blind HI survey. The total LF of the HI selected sample is flat, with Schechter parameters M*=-19.38_{-0.62}^{+1.02} + 5 log h mag and…
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…
In many polarimetry applications, including observations in the X-ray band, the measurement of a polarization signal can be reduced to the detection and quantification of a deviation from uniformity of a distribution of measured angles. We…
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)…
According to quantum theory, two ensembles of quantum systems that are described by the same density operator are indistinguishable. For example, unpolarized light can be obtained either by an incoherent mixture of two orthogonal pure…
Consider randomly picked points inside the n-dimensional unit hypersphere centered at the origin of the Cartesian coordinate system. The Cartesian coordinates of the points are random variables, which form an n-dimensional vector for each…
This work is aimed at quantifying the uncertainties in the 3D reconstruction of the location of coronal mass ejections (CMEs) obtained with the polarization ratio technique. The method takes advantage of the different distributions along…
We propose a new method to analyse the alignment of optical polarisation vectors from quasars. This method leads to a definition of intrinsic preferred axes and to a determination of the probability $p^{\sigma}$ that the distribution of…
We attract attention to the fact that the ultimate (shot-noise-limited) polarimetric sensitivity can be enhanced by orders of magnitude leaving the photon flux incident onto the photodetector on the same low level. This opportunity is of…
We investigated numerically the relationship between the lasing threshold, the density of states (DOS), and field localization in 1D photonic crystals (PC) for off-axis laser action. The angular dependence of the corresponding quantities…
We investigate the discrimination between photon polarizations when measured by moving detectors. Both unambiguous and minimum-error discriminations are considered, and we analyze the the optimal successful (correct) probability as a…
We present parton distribution functions which include a quantitative estimate of its uncertainties. The parton distribution functions are optimized with respect to deep inelastic proton data, expressing the uncertainties as a density…
Lensing probabilities of quasars with image separations greater than \Delta\theta and flux density ratios less than q_{\mathrm{r}} are calculated by foreground dark matter halos in a flat, cosmological constant dominated (\LambdaCDM)…
The exact homogenized probability density function, for a photon making a step of length $s$ has been analytically derived for a binary (isotropic-Poisson) statistical mixture with unmatched refractive indexes. The companions, exact,…
We study the reliability of dark matter (DM) profile determinations for rich clusters of galaxies based on weak gravitational lensing measurements. We consider three functional forms for the mass distribution: a softened isothermal sphere…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
We derive a simple and precise approximation to probability density functions in sampling distributions based on the Fourier cosine series. After clarifying the required conditions, we illustrate the approximation on two examples: the…
Studying the longitudinally polarized fraction of $W^\pm W^\pm$ scattering at the LHC is crucial to examine the unitarization mechanism of the vector boson scattering amplitude through Higgs and possible new physics. We apply here for the…