相关论文: Cumulants of products of Normally distributed rand…
Cumulants linearize convolution of measures. We use a formula of Good to define noncommutative cumulants in a very general setting.It turns out that the essential property needed is exchangeability of random variables. Roughly speaking the…
We consider a generalization of information density to a partitioning into $N \geq 2$ subvectors. We calculate its cumulant-generating function and its cumulants, showing that these quantities are only a function of all the regression…
Factorial moments and cumulants are usually defined with respect to the unconditioned Poisson process. Conditioning a sample by selecting events of a given overall multiplicity $N$ necessarily introduces correlations. By means of Edgeworth…
We study how Boolean cumulants can be used in order to address operations with freely independent random variables, particularly in connection to the $*$-distribution of the product of two selfadjoint freely independent random variables,…
Computing moments of various parameter estimators related to an autoregressive model of Statistics, one needs to evaluate several expressions of the type mentioned in the title of this article. We proceed to derive the corresponding…
In the linear random effects model, when distributional assumptions such as normality of the error variables cannot be justified, moments may serve as alternatives to describe relevant distributions in neighborhoods of their means.…
The purpose of the present paper is to establish moment estimates of Rosenthal type for a rather general class of random variables satisfying certain bounds on the cumulants. We consider sequences of random variables which satisfy a central…
This paper illustrates how to calculate the moments and cumulants of the two-stage Mann-Whitney statistic. These results may be used to calculate the asymptotic critical values of the two-stage Mann-Whitney test. In this paper, a large…
The survey is dedicated to a celebrated series of quantitave results, developed by the Lithuanian school of probability, on the normal approximation for a real-valued random variable. The key ingredient is a bound on cumulants of the type…
Cumulants and moments are closely related to the basic mathematics of continuous and discrete selection (respectively). These relationships generalize Fisher's fundamental theorem of natural selection and also make clear some of its…
This survey provides a unified discussion of multiple integrals, moments, cumulants and diagram formulae associated with functionals of completely random measures. Our approach is combinatorial, as it is based on the algebraic formalism of…
The moments of random variables are fundamental statistical measures for characterizing the shape of a probability distribution, encompassing metrics such as mean, variance, skewness, and kurtosis. Additionally, the product moments,…
Cumulants are a notion that comes from the classical probability theory, they are an alternative to a notion of moments. We adapt the probabilistic concept of cumulants to the setup of a linear space equipped with two multiplication…
We continue the investigation of noncommutative cumulants. In this paper various characterizations of noncommutative Gaussian random variables are proved.
Exponential distributions appear in a wide range of applications including chemistry, nuclear physics, time series analyses, and stock market trends. There are conceivable circumstances in which one would be interested in the cumulative…
We derive a formula which expresses a second order cumulant whose entries are products as a sum of cumulants where the entries are single factors. This extends to the second order case the formula of Krawczyk and Speicher. We apply our…
In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…
In the setting of polynomial jump-diffusion dynamics, we provide an explicit formula for computing correlators, namely, cross-moments of the process at different time points along its path. The formula appears as a linear combination of…
Shape dependence of higher order correlations introduces complication in direct determination of these quantities. For this reason theoretical and observational progress has been restricted in calculating one point distribution functions…
We prove a formula to express multivariate monotone cumulants of random variables in terms of their moments by using a Hopf algebra of decorated Schr\"oder trees.