Related papers: Non-Gaussian Chi-squared method with the multivari…
The random vector of frequencies in a generalized urn model is viewed as conditionally independent random variables, given their sum. Such a representation is exploited to derive Edgeworth expansions for a sum of functions of such…
Non-Gaussian distributions of cosmic microwave background (CMB) anisotropies have been proposed to reconcile the discrepancies between different experiments at half-degree scales (Coulson et al. 1994). Each experiment probes a different…
We demonstrate that the most probable state of a conserved system with a limited number of entities or molecules is the state where non-Gaussian and non-chi-square distributions govern. We have conducted a thought experiment using a…
We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with $t$ marginals obtained through scale…
In this paper, we derive a valid Edgeworth expansions for the Bessel corrected empirical variance when data are generated by a strongly mixing process whose distribution can be arbitrarily. The constraint of strongly mixing process makes…
The complex Gaussian distribution has been widely used as a fundamental spectral and noise model in signal processing and communication. However, its Gaussian structure often limits its ability to represent the diverse amplitude…
Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…
Nonlinear regression analysis is a popular and important tool for scientists and engineers. In this article, we introduce theories and methods of nonlinear regression and its statistical inferences using the frequentist and Bayesian…
The family of q-Gaussian and q-exponential probability densities fit the statistical behavior of diverse complex self-similar non-equilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained…
In order to quantify higher-order correlations of the galaxy cluster distribution we use a complete family of additive measures which give scale-dependent morphological information. Minkowski functionals can be expressed analytically in…
In this paper we study the large deviations of time averaged mean square displacement (TAMSD) for Gaussian processes. The theory of large deviations is related to the exponential decay of probabilities of large fluctuations in random…
Applying the standard weighted mean formula, [sum_i {n_i sigma^{-2}_i}] / [sum_i {sigma^{-2}_i}], to determine the weighted mean of data, n_i, drawn from a Poisson distribution, will, on average, underestimate the true mean by ~1 for all…
We show how observations of the evolution of the galaxy cluster number abundance can be used to constrain primordial non-Gaussianity in the universe. We carry out a maximum likelihood analysis incorporating a number of current datasets and…
Gaussian cosmic microwave background skies are fully specified by the power spectrum. The conventional method of characterizing non-Gaussian skies is to evaluate higher order moments, the n-point functions and their Fourier transforms. We…
Recently, several studies proposed non-linear transformations, such as a logarithmic or Gaussianization transformation, as efficient tools to recapture information about the (Gaussian) initial conditions. During non-linear evolution, part…
Many applications of Gaussian random fields and Gaussian random processes are limited by the computational complexity of evaluating the probability density function, which involves inverting the relevant covariance matrix. In this work, we…
Although using non-Gaussian distributions in economic models has become increasingly popular, currently there is no systematic way for calibrating a discrete distribution from the data without imposing parametric assumptions. This paper…
We compare the latest results from CMB experiments at scales around $l_e \sim 150$ over different parts of the sky to test the hypothesis that they are drawn from a Gaussian distribution, as is usually assumed. Using both the diagonal and…
We compute the skewness of the matter distribution arising from non-linear evolution and from non-Gaussian initial perturbations. We apply our result to a very generic class of models with non-Gaussian initial conditions and we estimate…
In this paper, we use the empirical likelihood method to construct the confidence regions for the difference between the parameters of a two-phases nonlinear model with random design. We show that the empirical likelihood ratio has an…