相关论文: Means of a Dirichlet process and multiple hypergeo…

In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…

We define the $L$-measure on the set of Dirichlet characters as an analogue of the Plancherel measure, once considered as a measure on the irreducible characters of the symmetric group. We compare the two measures and study the limit in…

We obtain the optimal proxy variance for the sub-Gaussianity of Beta distribution, thus proving upper bounds recently conjectured by Elder (2016). We provide different proof techniques for the symmetrical (around its mean) case and the…

At present, the fundamental solutions of the multidimensional elliptic equation with the several singular coefficients are known and they are expressed in terms of the Lauricella hypergeometric function of many variables. In this paper we…

We calculate murmuration densities for two families of Dirichlet characters. The first family contains complex Dirichlet characters normalized by their Gauss sums. Integrating the first density over a geometric interval yields a murmuration…

The class of Dirichlet series associated with a periodic arithmetical function $f$ includes the Riemann zeta-function as well as Dirichlet $L$-functions to residue class characters. We study the value-distribution of these Dirichlet series…

We study diffusion processes and stochastic flows which are time-changed random perturbations of a deterministic flow on a manifold. Using non-symmetric Dirichlet forms and their convergence in a sense close to the Mosco-convergence, we…

In the present paper new insights into the study of the Non-central Dirichlet distribution are provided. This latter is the analogue of the Dirichlet distribution obtained by replacing the Chi-Squared random variables involved in its…

Most metrics between finite point measures currently used in the literature have the flaw that they do not treat differing total masses in an adequate manner for applications. This paper introduces a new metric $\bar{d}_1$ that combines…

When analyzing data from multiple sources, it is often convenient to strike a careful balance between two goals: capturing the heterogeneity of the samples and sharing information across them. We introduce a novel framework to model a…

In his 1986 book, Aitchison explains that compositional data is regularly mishandled in statistical analyses, a pattern that continues to this day. The Dirichlet Type I distribution is a multivariate distribution commonly used to model a…

An approach will be proposed to determine the existence of a limit distribution of additive arithmetic functions in this work. It is based on assertions that will be proven in this work and on the properties of Dirichlet convolution and…

We extend the definition of the Lerch distribution to the set of nonnegative integers for greater applicability to modeling count data. We express its properties in terms of Lerch's transcendent, and study its unimodality, hazard function…

Nonparametric mixture models based on the Dirichlet process are an elegant alternative to finite models when the number of underlying components is unknown, but inference in such models can be slow. Existing attempts to parallelize…

Exact expressions are given for the distribution function of the ratio of a weighted sum of independent chi-squared variables to a single chi-square variable, scaled appropriately. This distribution is the generalization of the classical F…

We establish upper bounds for shifted moments of cubic and quartic Dirichlet $L$-functions under the generalized Riemann hypothesis. As an application, we prove bounds for moments of cubic and quartic Dirichlet character sums.

We describe a procedure to introduce general dependence structures on a set of Dirichlet processes. Dependence can be in one direction to define a time series or in two directions to define spatial dependencies. More directions can also be…

Bayesian nonparametric statistics is an area of considerable research interest. While recently there has been an extensive concentration in developing Bayesian nonparametric procedures for model checking, the use of the Dirichlet process,…

The theory of distributions provides generalized solutions for problems which do not have a classical solution. However, there are problems which do not have solutions, not even in the space of distributions. As model problem you may think…

In public health management there is a need to produce subnational estimates of health outcomes. Often, however, funds are not available to collect samples large enough to produce traditional survey sample estimates for each subnational…