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Degree distribution models are incredibly important tools for analyzing and understanding the structure and formation of social networks, and can help guide the design of efficient graph algorithms. In particular, the Power-law degree…
Many high dimensional vector distances tend to a constant. This is typically considered a negative "contrast-loss" phenomenon that hinders clustering and other machine learning techniques. We reinterpret "contrast-loss" as a blessing.…
High-dimensional sample correlation matrices are a crucial class of random matrices in multivariate statistical analysis. The central limit theorem (CLT) provides a theoretical foundation for statistical inference. In this paper, assuming…
In this paper a new lifetime distribution which is obtained by compounding Lindley and geometric distributions, named Lindley-geometric (LG) distribution, is introduced. Several properties of the new distribution such as density, failure…
In this paper, we discuss the joint value distribution of $L$-functions in a suitable class. We obtain joint large deviations results in the central limit theorem for these $L$-functions and some mean value theorems, which give evidence…
Power-law distributions occur in wide variety of physical, biological, and social phenomena. In this paper, we propose a statistical hypothesis test based on the log-likelihood ratio to assess whether two samples of discrete data are drawn…
We show that a knowledge of diagonal partons at a low scale is sufficient to determine the off-diagonal (or skewed) distributions at a higher scale, to a good degree of accuracy. We quantify this observation by presenting results for the…
Using the SLS technique, the size distribution can be measured accurately when the Rayleigh-Gans-Debye approximation is valid for dilute homogenous spherical particles in dispersion. For the commercial samples, the static sizes are…
Both observational and theoretical research over the past decade has demonstrated that the probability distribution function (PDF) of the gas density in turbulent molecular clouds is a key ingredient for understanding star formation. It has…
It is shown that the distribution functions of the diffusion coefficient are very similar in the standard model of quantum diffusion in a disordered metal and in a model of classical diffusion in a disordered medium: in both cases the…
We investigate the positivity of double parton distributions with a non-trivial dependence on the parton colour. It turns out that positivity is not preserved by leading-order evolution from lower to higher scales, in contrast to the case…
The log-Lindley distribution was recently introduced in the literature as a viable alternative to the Beta distribution. This distribution has a simple structure and possesses useful theoretical properties relevant in insurance. Classical…
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…
In this paper we provide an asymptotic theory for the symmetric version of the Kullback--Leibler (KL) divergence. We define a estimator for this divergence and study its asymptotic properties. In particular, we prove Law of Large Numbers…
We introduce and study the r-Lah distribution whose definition involves r-Stirling numbers of both kinds. We compute its expectation and variance, show its log-concavity and prove limit theorems for this distribution. We use these results…
The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question…
The Fourier representation for the uniform distribution over the Boolean cube has found numerous applications in algorithms and complexity analysis. Notably, in learning theory, learnability of Disjunctive Normal Form (DNF) under uniform as…
We propose a test based on the theory of algorithmic complexity and an experimental evaluation of Levin's universal distribution to identify evidence in support of or in contravention of the claim that the world is algorithmic in nature. To…
In studies of maternal exposure to air pollution a children's health outcome is regressed on exposures observed during pregnancy. The distributed lag nonlinear model (DLNM) is a statistical method commonly implemented to estimate an…
Quantifying distributional separation across groups is fundamental in statistical learning and scientific discovery, yet most classical discrepancy measures are tailored to two-group comparisons. We generalize the underlap coefficient…