Related papers: A note on sum and difference of correlated chi-squ…
In this article, we develop a distributed variable screening method for generalized linear models. This method is designed to handle situations where both the sample size and the number of covariates are large. Specifically, the proposed…
The paper applies the theory developed in Part I to the discrete normal approximation in total variation of random vectors in ${\mathbb Z}^d$. We illustrate the use of the method for sums of independent integer valued random vectors, and…
The geometric sum plays a significant role in risk theory and reliability theory \cite{Kala97} and a prototypical example of the geometric sum is R\'enyi's theorem~\cite{Renyi56} saying a sequence of suitably parameterised geometric sums…
In this paper, we propose a new distribution with unitary support which can be characterized as a ratio of the type $W=X_1/(X_1+X_2)$, where $(X_1, X_2)^\top$ follows a bivariate extreme distribution with Fr\'echet margins, that is, $X_1$…
Histograms with weighted entries are used to estimate probability density functions. Computer simulation is the main application of this type of histograms. A review on chi-square tests for comparing weighted histograms is presented in this…
We consider component-wise equivariant estimation of order restricted location/scale parameters of a general bivariate distribution under quite general conditions on underlying distributions and the loss function. This paper unifies various…
We propose extensions and improvements of the statistical analysis of distributed multipoles (SADM) algorithm put forth by Chipot et al. in [6] for the derivation of distributed atomic multipoles from the quantum-mechanical electrostatic…
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…
The variance-gamma (VG) distributions form a four-parameter family which includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and distributional…
We derive closed form expressions for the lower expectations that correspond to total variation distance and chi-squared divergence balls around a probability mass function over a finite set.
This article proposes a bivariate Simplex distribution for modeling continuous outcomes constrained to the interval $(0,1)$, which can represent proportions, rates, or indices. We derive analytical expressions to calculate the dependence…
Variance partitioning methods, which are built upon multivariate statistics, have been widely applied in different taxa and habitats in community ecology. Here, I performed a literature review on the development and application of the…
This article compares the distributions of integer-valued random variables and Poisson random variables. It considers the total variation and the Wasserstein distance and provides, in particular, explicit bounds on the pointwise difference…
Statistical divergences are ubiquitous in machine learning as tools for measuring discrepancy between probability distributions. As these applications inherently rely on approximating distributions from samples, we consider empirical…
The bivariate Gaussian distribution has been a key model for many developments in statistics. However, many real-world phenomena generate data that follow asymmetric distributions, and consequently bivariate normal model is inappropriate in…
Several methods have been proposed to approximate the sum of correlated lognormal RVs. However the accuracy of each method relies highly on the region of the resulting distribution being examined, and the individual lognormal parameters,…
The XGamma distribution is a generated distribution from a mixture of Exponential and Gamma distributions. It is found that in many cases the XGamma has more flexibility than the Exponential distribution. In this paper we consider the sum…
We investigate the problem of finding necessary and sufficient conditions for convergence in distribution towards a general finite linear combination of independent chi-squared random variables, within the framework of random objects living…
The mathematics of linear fits is presented in covariant form. Topics include: correlated data, covariance matrices, joint fits to multiple data sets, constraints, and extension of the formalism to non-linear fits. A brief summary at the…
We derive the exponential as well as power decreasing tail estimations for normed sums of centered independent identical distributed (or not) random variables on the Khintchine's form. We consider arbitrary, in particular, non-Rademacher's…