相关论文: Three series theorem for independent random variab…

We adapt arguments concerning entropy-theoretic convergence from the independent case to the case of FKG random variables. FKG systems are chosen since their dependence structure is controlled through covariance alone, though in the sequel…

We show that, for two non-trivial random variables X and Y under a sublinear expectation space, if X is independent from Y and Y is independent from X, then X and Y must be maximally distributed.

This is a chapter for the forthcoming New Handbook of Mathematical Psychology, to be published by Cambridge University Press. A systematic theory of random variables and joint distributions under varying conditions is presented. This is a…

We present some product representations for random variables with the Linnik, Mittag-Leffler and Weibull distributions and establish the relationship between the mixing distributions in these representations. Based on these representations,…

We present a general central limit theorem with simple, easy-to-check covariance-based sufficient conditions for triangular arrays of random vectors when all variables could be interdependent. The result is constructed from Stein's method,…

Given natural parameters s and r, where $2\leq s\leq r$, we consider the distribution of a random variable $\xi=\sum\limits_{k=1}^{\infty}s^{-k}\xi_k\equiv\Delta^{r_s}_{\xi_1\xi_2...\xi_k...},$ where $(\xi_k)$ is a sequence of independent…

A mathematical framework for information-theoretic analysis is established, with a new viewpoint of describing transmitted messages and communication channels by the nonlinear expectation theory, beyond the framework of classical…

In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The…

The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…

We give a simple and general central limit theorem for a triangular array of m-dependent variables. The result requires only a Lindeberg condition and avoids unnecessary extra conditions that have been used earlier. The result applies also…

By well known results of probability theory, any sequence of random variables with bounded second moments has a subsequence satisfying the central limit theorem and the law of the iterated logarithm in a randomized form. In this paper we…

In this paper, we prove the equivalent conditions of complete moment convergence of the maximum for partial weighted sums of independent, identically distributed random variables under sublinear expectations space. As applications, the…

We establish two theorems for assessing the accuracy in total variation of multivariate discrete normal approximation to the distribution of an integer valued random vector $W$. The first is for sums of random vectors whose dependence…

Triangular distributions are a well-known class of distributions that are often used as an elementary example of a probability model. Maximum likelihood estimation of the mode parameter of the triangular distribution over the unit interval…

We give error estimates in Peng's central limit theorem for not necessarily nondegenerate case. The exposition uses the language of the classical probability theory instead of the language of the theory of sublinear expectations. We only…

Complex continuous or mixed joint distributions (e.g., P(Y | z_1, z_2, ..., z_N)) generally lack closed-form solutions, often necessitating approximations such as MCMC. This paper proposes Indeterminate Probability Theory (IPT), which makes…

Renyi's "thinning" operation on a discrete random variable is a natural discrete analog of the scaling operation for continuous random variables. The properties of thinning are investigated in an information-theoretic context, especially in…

We justify and discuss expressions for joint lower and upper expectations in imprecise probability trees, in terms of the sub- and supermartingales that can be associated with such trees. These imprecise probability trees can be seen as…

In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…

Taking the Fourier integral theorem as our starting point, in this paper we focus on natural Monte Carlo and fully nonparametric estimators of multivariate distributions and conditional distribution functions. We do this without the need…