Related papers: Probability density function of the Cartesian x-co…
The spectrum profile that emerges in molecular spectroscopy and atmospheric radiative transfer as the combined effect of Doppler and pressure broadenings is known as the Voigt profile function. Because of its convolution integral…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
We study the statistical properties of the gravitational field generated by galaxy distribution observed bythe Sloan Digital Sky Survey (DR7). We characterize the probability density function of gravitational force fluctuations and relate…
In this paper we obtain the density function and the distribution function of the distance between two uniformly and independently distributed random points in any right-angled triangle. The density function is derived from the chord length…
We consider the signed density of the extremal points of (two-dimensional) scalar fields with a Gaussian distribution. We assign a positive unit charge to the maxima and minima of the function and a negative one to its saddles. At first, we…
One possible way to investigate the nature of the primordial power spectrum fluctuations is by investigating the statistical properties of the local maximum in the density fluctuation fields. In this work we present a study of the mean…
A generalization of the classic Gaussian random variable to the family of Multi- Gaussian (MG) random variables characterized by shape parameter M > 0, in addition to the mean and the standard deviation, is introduced. The probability…
We study local power fluctuations in numerical simulations of stationary, homogeneous, isotropic turbulence in two and three dimensions with Gaussian forcing. Due to the near-Gaussianity of the one-point velocity distribution, the…
In [3], algorithms to compute the density of the distance to a random variable uniformly distributed in (a) a ball, (b) a disk, (c) a line segment, or (d) a polygone were introduced. For case (d), the algorithm, based on Green's theorem,…
Context. Whenever correlation functions are used for inference about cosmological parameters in the context of a Bayesian analysis, the likelihood function of correlation functions needs to be known. Usually, it is approximated as a…
Critical points of a scalar quantitiy are either extremal points or saddle points. The character of the critical points is determined by the sign distribution of the eigenvalues of the Hessian matrix. For a two-dimensional homogeneous and…
We perform high resolution ray-tracing simulations to investigate probability distribution functions (PDFs) of lensing convergence, shear, and magnification on distant sources up to the redshift of $z_s=20$. We pay particular attention to…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
We derive the isoperimetric profile of Gaussian type for an absolutely continuous probability measure on Euclidean spaces with respect to the Lebesgue measure, whose density is a radial function.The key is a generalization of the Poincar\'e…
An expression for the joint probability distribution of the principal curvatures at an arbitrary point in the ensemble of isosurfaces defined on isotropic Gaussian random fields on Rn is derived. The result is obtained by deriving symmetry…
The one-point probability distribution function (pdf) of the large-scale density field is an important tool to follow the evolution of cosmological structures. In this paper we present a new model for this pdf for all regimes and all…
Generalized quantum measurements with N distinct outcomes are used for determining the density matrix, of order d, of an ensemble of quantum systems. The resulting probabilities are represented by a point in an N-dimensional space. It is…
In the d dimensional Euclidean space, any set of n+1 independent random points, uniformly distributed in the interior of a unit ball of center O, determines almost surely a circumsphere of center C and of radius R, with n positive and less…
The distribution of the sum of r-th power of standard normal random variables is a generalization of the chi-squared distribution. In this paper, we represent the probability density function of the random variable by an one-dimensional…
In a search for the signature of turbulence in the diffuse interstellar medium in gas density distributions, we determined the probability distribution functions (PDFs) of the average volume densities of the diffuse gas. The densities were…