Related papers: Mean, Variance and Asymptotic Property for General…
Fisheries scientists use regression models to estimate population quantities, such as biomass or abundance, for use in climate, habitat, stock, and ecosystem assessments. However, these models are sensitive to the chosen probability…
This work explores the bounds of the variance of unilaterally truncated Gaussian distributions (UTGDs) and scaled chi distributions (UTSCDs) with fixed means. For any arbitrary Gaussian distribution function, $f(x;\mu,\sigma)$, with a…
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
Hyperbolic space is a geometry that is known to be well-suited for representation learning of data with an underlying hierarchical structure. In this paper, we present a novel hyperbolic distribution called \textit{pseudo-hyperbolic…
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the product $XY$ is derived. Some basic distributional properties are also derived, including…
In a two-way contingency table analysis with explanatory and response variables, the analyst is interested in the independence of the two variables. However, if the test of independence does not show independence or clearly shows a…
This paper generalizes the traditional statistical concept of prediction intervals for arbitrary probability density functions in high-dimensional feature spaces by introducing significance level distributions, which provides…
This chapter presents key concepts and theoretical results for analyzing estimation and inference in high-dimensional models. High-dimensional models are characterized by having a number of unknown parameters that is not vanishingly small…
In this paper we estimate the mean-variance portfolio in the high-dimensional case using the recent results from the theory of random matrices. We construct a linear shrinkage estimator which is distribution-free and is optimal in the sense…
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
We propose a high dimensional mean test framework for shrinking random variables, where the underlying random variables shrink to zero as the sample size increases. By pooling observations across overlapping subsets of dimensions, we…
Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the…
An approach to build Probabilistic Arithmetic in which initial values of all correlated random variables are known, but with varying degrees of accuracy. As a result of the proposed Probabilistic Arithmetic operations, variable values,…
A generalization of the classic Gaussian random variable to the family of Multi- Gaussian (MG) random variables characterized by shape parameter M > 0, in addition to the mean and the standard deviation, is introduced. The probability…
A symmetric random variable is called a Gaussian mixture if it has the same distribution as the product of two independent random variables, one being positive and the other a standard Gaussian random variable. Examples of Gaussian mixtures…
In Statistical Relational Artificial Intelligence, a branch of AI and machine learning which combines the logical and statistical schools of AI, one uses the concept {\em para\-metrized probabilistic graphical model (PPGM)} to model…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
In this study, a numerical quadrature for the generalized inverse Gaussian distribution is derived from the Gauss-Hermite quadrature by exploiting its relationship with the normal distribution. The proposed quadrature is not Gaussian, but…