Related papers: Moments of the complex multivariate normal distrib…
We discuss the probabilistic properties of the variation based third and fourth moments of financial returns as estimators of the actual moments of the return distributions. The moment variations are defined under non-parametric assumptions…
We develop moment estimators for the parameters of affine stochastic volatility models. We first address the challenge of calculating moments for the models by introducing a recursive equation for deriving closed-form expressions for…
We derive the joint distribution of the moments $\mathrm{Tr}\, Q^{\kappa}$ ($\kappa\geq0$) of the Wigner-Smith matrix for a chaotic cavity supporting a large number of scattering channels $n$. This distribution turns out to be…
Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete…
Principal Moment Analysis is a method designed for dimension reduction, analysis and visualization of high dimensional multivariate data. It generalizes Principal Component Analysis and allows for significant statistical modeling…
Descriptive statistics for parametric models are currently highly sensative to departures, gross errors, and/or random errors. Here, leveraging the structures of parametric distributions and their central moment kernel distributions, a…
We give necessary and sufficient conditions to characterize the convergence in distribution of a sequence of arbitrary random variables to a probability distribution which is the invariant measure of a diffusion process. This class of…
Risk assessment for rare events is essential for understanding systemic stability in complex systems. As rare events are typically highly correlated, it is important to study heavy-tailed multivariate distributions of the relevant…
We consider two random variables $X$ and $Y$ following correlated Gamma distributions, characterized by identical scale and shape parameters and a linear correlation coefficient $\rho$. Our focus is on the parameter: \[ D(X,Y) = \frac{|X -…
We consider a class of sample covariance matrices of the form $Q=TXX^{*}T^*,$ where $X=(x_{ij})$ is an $M \times N$ rectangular matrix consisting of i.i.d entries and $T$ is a deterministic matrix satisfying $T^*T$ is diagonal. Assuming $M$…
This paper provides closed-form expansions for the log-likelihood function of multivariate diffusions sampled at discrete time intervals. The coefficients of the expansion are calculated explicitly by exploiting the special structure…
Recently the identity method was proposed to calculate second moments of the multiplicity distributions from event-by-event measurements in the presence of the effects of incomplete particle identification. In this paper the method is…
We study the joint distribution of random abelian and non-abelian groups. In the abelian case, we prove several universality results for the joint distribution of the multiple cokernels for random $p$-adic matrices. In the non-abelian case,…
Moment matching is an easy-to-implement and usually effective method to reduce variance of Monte Carlo simulation estimates. On the other hand, there is no guarantee that moment matching will always reduce simulation variance for general…
In many practical situations we would like to estimate the covariance matrix of a set of variables from an insufficient amount of data. More specifically, if we have a set of $N$ independent, identically distributed measurements of an $M$…
A class of multivariate spectral representations for real-valued nonstationary random variables is introduced, which is characterised by a general complex Gaussian distribution. In this way, the temporal signal properties -- harmonicity,…
In this article, we discuss a bivariate distribution whose conditionals are univariate binomial distributions and the marginals are not binomial that exhibits negative correlation. Some useful structural properties of this distribution…
We show first that there are intrinsic relationships among different conditions, old and recent, which lead to some general statements in both the Stieltjes and the Hamburger moment problems. Then we describe checkable conditions and prove…
Given $0<q<1,$ every absolutely continuous distribution can be described in two different ways: in terms of a probability density function and also in terms of a $q$-density. Correspondingly, it has a sequence of moments and a sequence of…
This paper develops a polynomial normal transformation model, whereby various non-normal probability distributions can be simulated by the standard normal distribution. Two methods are presented to determine the coefficients of polynomial…