Related papers: Non-Gaussian Chi-squared method with the multivari…
q-Gaussian distribution appear in many science areas where we can find systems that could be described within a nonextensive framework. Usually, a way to assert that these systems belongs to nonextensive framework is by means of numerical…
Various types of expansions in series of Chebyshev-Hermite polynomials currently used in astrophysics for weakly non-normal distributions are compared, namely the Gram-Charlier, Gauss-Hermite and Edgeworth expansions. It is shown that the…
For testing goodness of fit it is very popular to use either the chi square statistic or G statistics (information divergence). Asymptotically both are chi square distributed so an obvious question is which of the two statistics that has a…
In the context of upcoming large-scale structure surveys such as Euclid, it is of prime importance to quantify the effect of peculiar velocities on geometric probes. Hence the formalism to compute in redshift space the geometrical and…
In a thought-provoking paper, Efron (2011) investigated the merit and limitation of an empirical Bayes method to correct selection bias based on Tweedie's formula first reported by \cite{Robbins:1956}. The exceptional virtue of Tweedie's…
We consider gravitational clustering from primoridal non-Gaussian fluctuations provided by a $\chi^2$ model, as motivated by some models of inflation. The emphasis is in signatures that can be used to constrain this type of models from…
The aim of this paper is to extend Azzalini's method. This extension is done in two stages: consider two dependent and non-identically distributed random variables say $X_1$ and $X_2$; model the dependence between $X_1$ and $X_2$ by a…
The gravitational evolution of the cosmic one-point probability distribution function (PDF) has been estimated using an analytic approximation that combines gravitational perturbation theory with the Edgeworth expansion around a Gaussian…
The question of testing for equality in distribution between two linear models, each consisting of sums of distinct discrete independent random variables with unequal numbers of observations, has emerged from the biological research. In…
Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…
The non isotropic noncentral elliptical shape distributions via pseudo-Wishart distribution are founded. This way, the classical shape theory is extended to non isotropic case and the normality assumption is replaced by assuming a…
Non-Gaussian shapes, despite a linear form of the mean-squared displacement, have been observed for the displacement distribution in a large range of diffusive systems. Stochastic models for such "Brownian yet non-Gaussian" diffusion will…
This paper presents a novel approach for propagating uncertainties in dynamical systems building on high-order Taylor expansions of the flow and moment-generating functions (MGFs). Unlike prior methods that focus on Gaussian distributions,…
Non-Gaussian likelihoods are essential for modelling complex real-world observations but pose significant computational challenges in learning and inference. Even with Gaussian priors, non-Gaussian likelihoods often lead to analytically…
The Gaussian linear model provides a unique way to obtain the posterior probability distribution as well as the Bayesian evidence analytically. Considering the expansion rate data, the Gaussian linear model can be applied for $\Lambda$CDM,…
We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…
The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…
This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…
Very massive high redshift clusters can be used to constrain and test the Lambda CDM model. Taking into account the observational constraints of Jee et al. (2009) we have calculated the probability for the most massive cluster to be found…
Structure formation in our Universe creates non-Gaussian random fields that will soon be observed over almost the entire sky by the Euclid satellite, the Vera-Rubin observatory, and the Square Kilometre Array. An unsolved problem is how to…