Related papers: Estimators, escort probabilities, and phi-exponent…

We study the distribution P(\omega) of the random variable \omega = x_1/(x_1 + x_2), where x_1 and x_2 are the wealths of two individuals selected at random from the same tempered Paretian ensemble characterized by the distribution \Psi(x)…

We consider upper exponential bounds for the probability of the event that an absolute deviation of sample mean from mathematical expectation p is bigger comparing with some ordered level epsilon. These bounds include 2 coefficients {alpha,…

Power laws and power laws with exponential cut-off are two distinct families of distributions on the positive real half-line. In the present paper, we propose a unified treatment of both families by building a family of distributions that…

The preferential attachment (PA) model is a popular way of modeling dynamic social networks, such as collaboration networks. Assuming that the PA function takes a parametric form, we propose and study the maximum likelihood estimator of the…

The existing upper and lower bounds between entropy and error probability are mostly derived from the inequality of the entropy relations, which could introduce approximations into the analysis. We derive analytical bounds based on the…

Abstract argumentation offers an appealing way of representing and evaluating arguments and counterarguments. This approach can be enhanced by a probability assignment to each argument. There are various interpretations that can be ascribed…

Let $X$ be a random variable distributed according to the binomial distribution with parameters $n$ and $p$. It is shown that $P(X>EX)\ge1/4$ if $1>p\ge c/n$, where $c:=\ln(4/3)$, the best possible constant factor.

Clans are representations of generalized algebraic theories that contain more information than the finite-limit categories associated to the locally finitely presentable categories of models via Gabriel-Ulmer duality. Extending…

We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and…

We investigate stochastic comparisons between exponential family distributions and their mixtures with respect to the usual stochastic order, the hazard rate order, the reversed hazard rate order, and the likelihood ratio order. A general…

It is believed that, in the limit as the conductor tends to infinity, correlations between the zeros of elliptic curve $L$-functions averaged within families follow the distribution laws of the eigenvalues of random matrices drawn from the…

We consider the classical problem of learning, with arbitrary accuracy, the natural parameters of a $k$-parameter truncated \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We…

We present a general result giving us families of incomplete and boundedly complete families of discrete distributions. For such families, the classes of unbiased estimators of zero with finite variance and of parametric functions which…

We use some properties of orthogonal polynomials to provide a class of upper/lower variance bounds for a function $g(X)$ of an absolutely continuous random variable $X$, in terms of the derivatives of $g$ up to some order. The new bounds…

Chernoff information upper bounds the probability of error of the optimal Bayesian decision rule for $2$-class classification problems. However, it turns out that in practice the Chernoff bound is hard to calculate or even approximate. In…

We obtain new results concerning Lang-Trotter conjecture on Frobenius traces and Frobenius fields over single and double parametric families of elliptic curves. We also obtain similar results with respect to the Sato-Tate conjecture. In…

Exponential families are a particular class of statistical manifolds which are particularly important in statistical inference, and which appear very frequently in statistics. For example, the set of normal distributions, with mean {\mu}…

We study minimization of a parametric family of relative entropies, termed relative $\alpha$-entropies (denoted $\mathscr{I}_{\alpha}(P,Q)$). These arise as redundancies under mismatched compression when cumulants of compressed lengths are…

Affiliation network is one kind of two-mode social network with two different sets of nodes (namely, a set of actors and a set of social events) and edges representing the affiliation of the actors with the social events. Although a number…

We study random normal matrix models whose eigenvalues tend to be distributed within a narrow "band" around the unit circle of width proportional to $\frac1n$, where $n$ is the size of matrices. For general radially symmetric potentials…