Related papers: Lognormal Property of Weak Lensing Fields
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 --…
We present the results of weak gravitational lensing statistics in four different cosmological $N$-body simulations. The data has been generated using an algorithm for the three-dimensional shear, which makes use of a variable softening…
Prior asymptotic performance analyses are based on the series expansion of the moment-generating function (MGF) or the probability density function (PDF) of channel coefficients. However, these techniques fail for lognormal fading channels…
A sample of eight quasars observed at high resolution and signal-to-noise is used to determine the probability distribution function (PDF), the power spectrum, and the correlation function of the transmitted flux in the \lya forest, in…
In many cosmological inference problems, the likelihood (the probability of the observed data as a function of the unknown parameters) is unknown or intractable. This necessitates approximations and assumptions, which can lead to incorrect…
We present the gauge-invariant formalism of cosmological weak lensing, accounting for all the relativistic effects due to the scalar, vector, and tensor perturbations at the linear order. While the light propagation is fully described by…
We use the spherical collapse (SC) approximation to derive expressions for the smoothed redshift-space probability distribution function (PDF), as well as the $p$-order hierarchical amplitudes $S_p$, in both real and redshift space. We…
This paper tackles the issue of real-time parametric estimation of a wide class of probability density functions from limited datasets. This type of estimation addresses recent applications that require joint sensing and actuation. The…
A comprehensive new approach is presented for deriving probability densities of physical properties characterizing lens or source that constitute an observed galactic microlensing event. While previously encountered problems are overcome,…
This expository note aims at illustrating weak convergence of probability measures from a broader view than a previously published paper. Though the results are standard for functional analysts, this approach is rarely known by…
The probability density function (PDF) associated with a given set of samples is approximated by a piecewise-linear polynomial constructed with respect to a binning of the sample space. The kernel functions are a compactly supported basis…
We use weak lensing data from the Hubble Space Telescope COSMOS survey to measure the second- and third-moments of the cosmic shear field, estimated from about 450,000 galaxies with average redshift <z> ~ 1.3. We measure two- and…
One of the consequences of entering the era of precision cosmology is the widespread adoption of photometric redshift probability density functions (PDFs). Both current and future photometric surveys are expected to obtain images of…
Herein, a methodology is developed to replicate functions, measures and stochastic processes onto a compact metric space. Many results are easily established for the replica objects and then transferred back to the original ones. Two…
The classical stochastic model of cosmology recently developed by us is reconsidered. In that approach the parameter $w$ defined by the equation of state $p=w{\rho}$ was taken to be fluctuating with mean zero and we compared the theoretical…
Observations of the Lyman-$\alpha$ forest in distant quasar spectra with upcoming surveys are expected to provide significantly larger and higher-quality datasets. To interpret these datasets, it is imperative to develop efficient…
We study the effect of the non-Gaussianity induced by gravitational evolution upon the statistical properties of absorption in quasar (QSO) spectra. Using the generic hierarchical ansatz and the lognormal approximation we derive the…
Several methods have been proposed to approximate the sum of lognormal RVs. However the accuracy of each method relies highly on the region of the resulting distribution being examined, and the individual lognormal parameters, i.e., mean…
Time series analysis allows for the determination of the Power Spectral Density (PSD) and Probability Density Function (PDF) for astrophysical sources. The former of these illustrates the distribution of power at various timescales,…
This paper outlines an approach to the approximation of probability density functions by quadratic forms of weighted orthonormal basis functions with positive semi-definite Hermitian matrices of unit trace. Such matrices are called…