相关论文: The maximum negative hypergeometric distribution

We study an urn model introduced in the paper of Chen and Wei, where at each discrete time step $m$ balls are drawn at random from the urn containing colors white and black. Balls are added to the urn according to the inspected colors,…

The paper deals with minimax optimal statistical tests for two composite hypotheses, where each hypothesis is defined by a non-parametric uncertainty set of feasible distributions. It is shown that for every pair of uncertainty sets of the…

Comparison of two univariate distributions based on independent samples from them is a fundamental problem in statistics, with applications in a wide variety of scientific disciplines. In many situations, we might hypothesize that the two…

We consider the problem of distinguishing between two arbitrary black-box distributions defined over the domain [n], given access to $s$ samples from both. It is known that in the worst case O(n^{2/3}) samples is both necessary and…

We prove a Gaussian process approximation for the sequence of random compositions of a two-color randomly reinforced urn for both the cases with the equal and unequal reinforcement means. By using the Gaussian approximation, the law of the…

A certain sampling process, concerning an urn with balls of two colors, proposed in 1965 by B.E. Oakley and R.L. Perry, and discussed by Peter Winkler and Martin Gardner, that has an extremely simple answer for the probability, namely the…

Based on the negative binomial model for the duration of wet periods measured in days, an asymptotic approximation is proposed for the distribution of the maximum daily precipitation volume within a wet period. This approximation has the…

We present a rapid method for the exact calculation of the cumulative distribution function of the maximum of multinomially distributed random variables. The method runs in time $O(mn)$, where $m$ is the desired maximum and $n$ is the…

Multivariate hypergeometric distribution arises frequently in elementary statistics and probability courses, for simultaneously studying the occurence law of specified events, when sampling without replacement from a finite population with…

Corresponding to $n$ independent non-negative random variables $X_1,...,X_n$, are values $M_1,...,M_n$, where each $M_i$ is the expected value of the maximum of $n$ independent copies of $X_i$. We obtain an upper bound to the expected value…

A 2-coloring of a hypergraph is a mapping from its vertices to a set of two colors such that no edge is monochromatic. Let $H_k(n,m)$ be a random $k$-uniform hypergraph on $n$ vertices formed by picking $m$ edges uniformly, independently…

We consider the problem of estimating the distribution underlying an observed sample of data. Instead of maximum likelihood, which maximizes the probability of the ob served values, we propose a different estimate, the high-profile…

Given a set of $n$ real numbers, if the sum of elements of every subset of size larger than $k$ is negative, what is the maximum number of subsets of nonnegative sum? In this note we show that the answer is $\binom{n-1}{k-1} +…

Recently W. Lao and M. Mayer [6], [7], [9] considered $U$-max - statistics, where instead of sum appears the maximum over the same set of indices. Such statistics often appear in stochastic geometry. The examples are given by the largest…

Necessary and sufficient conditions of uniform consistency are explored. A hypothesis is simple. Nonparametric sets of alternatives are bounded convex sets in $\mathbb{L}_p$, $p >1$ with "small" balls deleted. The "small" balls have the…

We study several basic problems about colouring the $p$-random subgraph $G_p$ of an arbitrary graph $G$, focusing primarily on the chromatic number and colouring number of $G_p$. In particular, we show that there exist infinitely many…

The unit ball random geometric graph $G=G^d_p(\lambda,n)$ has as its vertices $n$ points distributed independently and uniformly in the $d$-dimensional unit ball, with two vertices adjacent if and only if their $l_p$-distance is at most…

Unbiased estimation for parameters of maximal distribution is a very fundamental problem in the statistical theory of sublinear expectation. In this paper, we proved that the maximum estimator is the largest unbiased estimator for the upper…

The negative multinomial distribution is a multivariate generalization of the negative binomial distribution. In this paper, we consider the problem of estimating an unknown matrix of probabilities on the basis of observations of negative…

It is well known that in a small P\'olya urn, i.e., an urn where second largest real part of an eigenvalue is at most half the largest eigenvalue, the distribution of the numbers of balls of different colours in the urn is asymptotically…