Related papers: A new method for testing isotropy with Shannon ent…
We use the hemisphere comparison method to test the isotropy of the SnIa absolute magnitudes of the Pantheon+ and SH0ES samples in various redshift/distance bins. We compare the identified levels of anisotropy in each bin with Monte-Carlo…
We test the isotropy of the Hubble diagram. At small redshifts, this is possible without assumptions on the cosmic inventory and provides a fundamental test of the cosmological principle. At higher redshift we check for the self-consistency…
In this paper, we obtain a new characterization result for symmetric distributions based on the entropy measure. Using the characterization, we propose a nonparametric test to test the symmetry of a distribution. We also develop the…
We have presented a new axiomatic derivation of Shannon Entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function.We have then modified shannon entropy to take account…
The two-point angular correlation function is a traditional method used to search for deviations from expectations of isotropy. In this paper we develop and explore a statistically descriptive three-point method with the intended…
We quantify the degree of inhomogeneity in the Luminous Red Galaxy (LRG) distribution from the SDSS DR7 as a function of length scales by measuring the Shannon entropy in independent and regular cubic voxels of increasing grid sizes. We…
We introduce the problem of \emph{entropy equivalence testing} for probability distributions, a relaxation of the well-studied closeness testing problem, where the distribution testing algorithm is now only required to distinguish, given…
Reliable data-driven estimation of Shannon entropy from small data sets, where the number of examples is potentially smaller than the number of possible outcomes, is a critical matter in several applications. In this paper, we introduce a…
We propose several pseudoentropy measures that agree well with the Wehrl entropy, but are significantly faster to compute. All of them are rotationally invariant measures of entanglement very sensitive to non-Gaussianity, anisotropy, and…
We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that…
This paper proposes parametric and non-parametric hypothesis testing algorithms for detecting anisotropy -- rotational variance of the covariance function in random fields. Both algorithms are based on resampling mechanisms, which enable…
We present a novel approach to disentangle two key contributions to the largest-scale anisotropy of the galaxy distribution: (i) the intrinsic dipole due to clustering and anisotropic geometry, and (ii) the kinematic dipole due to our…
We use information entropy to analyze the anisotropy in the mock galaxy catalogues from dark matter distribution and simulated biased galaxy distributions from $\Lambda$CDM N-body simulation. We show that one can recover the linear bias…
Cosmography can be used to constrain the kinematics of universe in a model-independent way. In this work, we attempted to combine the Pad$\rm \acute{e}$ approximations with the latest Pantheon+ sample for testing cosmological principle.…
We test the isotropy of the expansion of the Universe by estimating the hemispherical anisotropy of supernova type Ia (SN Ia) Hubble diagrams at low redshifts (z<0.2). We compare the best fit Hubble diagrams in pairs of hemispheres and…
The problem of Shannon entropy estimation in countable infinite alphabets is addressed from the study and use of convergence results of the entropy functional, which is known to be discontinuous with respect to the total variation distance…
A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of the marginal distributions and the…
In many statistical studies, the measure of uncertainties like entropy, extropy, varentropy and varextropy of a distribution function is of prime interest. This paper proposes estimators of extropy and varextropy. Proposed estimators are…
We propose and implement a novel, robust, and non-parametric test of statistical isotropy of the expansion of the universe, and apply it to around one thousand type Ia supernovae from the Pantheon sample. We calculate the angular clustering…
We discuss some details regarding the method of smoothed residuals, which has recently been used to search for anisotropic signals in low-redshift distance measurements (Supernovae). In this short note we focus on some details regarding the…