Related papers: Fitting Probability Distribution Functions in Turb…

A method to approximate continuous multi-dimensional probability density functions (PDFs) using their projections and correlations is described. The method is particularly useful for event classification when estimates of systematic…

We develop a method to calculate the column density distribution of the Lyman-alpha forest for column densities in the range $10^{12.5} - 10^{14.5} cm^{-2}$. The Zel'dovich approximation, with appropriate smoothing, is used to compute the…

Despite the high accuracy of photometric redshifts (zphot) derived using Machine Learning (ML) methods, the quantification of errors through reliable and accurate Probability Density Functions (PDFs) is still an open problem. First, because…

In many classification problems it is desirable to output well-calibrated probabilities on the different classes. We propose a robust, non-parametric method of calibrating probabilities called SplineCalib that utilizes smoothing splines to…

We use the Delaunay Tessellation Field Estimator (DTFE) to study the one-point density distribution functions of the Millennium (MS) and Millennium-II (MS-II) simulations. The DTFE technique is based directly on the particle positions,…

We compare velocity structure in the Polaris Flare molecular cloud at scales ranging from 0.015 pc to 20 pc to simulations of supersonic hydrodynamic and MHD turbulence computed with the ZEUS MHD code. We use several different statistical…

We study density fluctuations in supersonic turbulence using both theoretical methods and numerical simulations. A theoretical formulation is developed for the probability distribution function (PDF) of the density at steady state,…

We present the first prediction of the probability distribution function (PDF) for self-organization of shear flows modeled by a nonlinear diffusion equation with a stochastic forcing. A novel non-perturbative method based on a coherent…

We propose a new, physically motivated fitting function for density PDFs in turbulent gas. Although it is known that when gas is isothermal, the PDF is approximately lognormal in the core, high-resolution simulations show large deviations…

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…

This paper investigates probability density functions (PDFs) that are continuous everywhere, nearly uniform around the mode of distribution, and adaptable to a variety of distribution shapes ranging from bell-shaped to rectangular. From the…

We derive cosmological constraints from the probability distribution function (PDF) of evolved large-scale matter density fluctuations. We do this by splitting lines of sight by density based on their count of tracer galaxies, and by…

Molecular clouds exhibit lognormal probability density functions (PDF) of mass densities, which are thought to arise as a consequence of isothermal, supersonic turbulence. Star formation is then widely assumed to occur in perturbations in…

We describe a simple method for estimating the vertical column density in Smoothed Particle Hydrodynamics (SPH) simulations of discs. As in the method of Stamatellos et al. (2007), the column density is estimated using pre-computed local…

While second and higher order correlations of the light distribution have received extensive study, the lowest order probability distribution function (PDF) -- the probability that a unit volume of space will emit a given amount of light --…

In some real world applications, such as spectrometry, functional models achieve better predictive performances if they work on the derivatives of order m of their inputs rather than on the original functions. As a consequence, the use of…

We propose a practical empirical fitting function to characterize the non-Gaussian displacement distribution functions (DispD) often observed for heterogeneous diffusion problems. We first test this fitting function with the problem of a…

The estimation of cumulative distribution functions (CDF) and probability density functions (PDF) is a fundamental practice in applied statistics. However, challenges often arise when dealing with data arranged in grouped intervals. In this…

We study the effects of radiative transfer on the Probability Distribution Functions (PDFs) of simulations of magnetohydrodynamic turbulence in the widely studied $^{13}$CO 2-1 transition. We find that the integrated intensity maps…

Distribution functions (DFs) for dynamically warm thin stellar disks residing in arbitrary axisymmetric potentials are presented which approximately reproduce pre-described surface-density and velocity-dispersion profiles. The functional…