We construct a d-dimensional discrete multivariate distribution for which any proper subset of its components belongs to a specific family of distributions. However, the joint d-dimensional distribution fails to belong to that family and in other words, it is ‘inconsistent’ with the distribution of these subsets. We also address preservation of this ‘inconsistency’ property for the symmetric Bi...

The basic message of this talk could have been delivered a long ago, may be even soon after the time of publication of classical papers of K. Pearson (1900) and R. A. Fisher (1922, 1924). However, the tradition of using the chi-square goodness of fit statistic became so widely spread, and the point of view that, for the case of discrete distributions, statistics “have to” have their asymptotic ...

We consider the problem of testing for differences among a number of discrete distributions. Our approach is based on viewing the different samples as drawn from a mixture distribution where each mixture component represents a different group or cluster. We adapt the methodology of Dasgupta and Raftery (1998) to this problem, giving explicit details in the case of multinomial and first-order Ma...

In this paper, we consider several efficient data structures for the problem of sampling from a dynamically changing discrete probability distribution, where some prior information is known on distribution rates, in particular maximum and minimum rate, number possible outcomes N large. We three basic structures, Acceptance-Rejection method, Complete Binary Tree Alias method. These can be used a...

In the last few decades many papers appeared in the statistical literature on the discretization of continuous distributions. The main reasons for discretizing a continuous distributions are two fold, namely, (i) the discrete analogue of a continuous distribution provide probability mass function (pmf) that can compete with the classical discrete distributions commonly used in the statistical a...

In the last few decades many papers appeared in the statistical literature on the discretization of continuous distributions. The main reasons for discretizing a continuous distributions are two fold, namely, (i) the discrete analogue of a continuous distribution provide probability mass function (pmf) that can compete with the classical discrete distributions commonly used in the statistical a...

in this paper, the interaction between an oscillating dipole moment and a silver nanoparticle has been studied. our calculations are based on mie scattering theory and discrete dipole approximation(dda) method.at first, the resonance frequency due to excitingthe localized surface plasmons has been obtained using mie scattering theory and then by exciting a dipole moment in theclose proximity of...

A new method of texture modelling based on discrete distribution mixtures is proposed. Unlike some alternative approaches the statistical properties of textures are modelled by a discrete distribution mixture of product components. The univariate distributions in the products are represented in full generality by vectors of probabilities without any constraints. The texture analysis is made in ...

As argued in the proof sketch of Theorem 2, it suffices to show that r ,ε,k,n (Q) obeys the data processing inequality. is the minimax risk in the non-private setting.

We study and compare three estimators of a discrete monotone distribution: (a) the (raw) empirical estimator; (b) the "method of rearrangements" estimator; and (c) the maximum likelihood estimator. We show that the maximum likelihood estimator strictly dominates both the rearrangement and empirical estimators in cases when the distribution has intervals of constancy. For example, when the distr...