Expressing the largest eigenvalue of a singular beta F-matrix with heterogeneous hypergeometric functions

Heterogeneous hypergeometric functions with two matrix arguments and the exact distribution of the largest eigenvalue of a singular beta-Wishart matrix

This paper discusses certain properties of heterogeneous hypergeometric functions with two matrix arguments. These functions are newly defined but have already appeared in statistical literature and are useful when dealing with the derivation of certain distributions for the eigenvalues of singular beta-Wishart matrices. The joint density function of the eigenvalues and the distribution of the largest eigenvalue can be expressed in terms of certain heterogeneous hypergeometric functions. Exact computation of the distribution of the largest eigenvalue is conducted here for a real case.

Some Relationships and Properties of the Hypergeometric Distribution

The binomial and Poisson distributions have interesting relationships with the beta and gamma distributions, respectively, which involve their cumulative distribution functions and the use of conjugate priors in Bayesian statistics. We briefly discuss these relationships and some properties resulting from them which play an important role in the construction of exact nested two-sided confidence intervals and the computation of two-tailed P-values. The purpose of this article is to show that such relationships also exist between the hypergeometric distribution and a special case of the Polya (o…

定向高斯超几何β分布及其在受污染二元抽样中的应用

Directional Gaussian hypergeometric beta distributions and their uses in contaminated binary sampling

该研究对高斯超几何β分布进行重参数化并分为左右定向变体，明确其为特定受污染二元模型的合适后验分布，推导了相关性质与计算方法，可用于受污染二元抽样的贝叶斯推断。

Certain Family of Some Beta Distributions Arising from Distribution of Randomly Weighted Average

We give the exact distribution of the average of n independent beta random variables weighted by the selected cuts of (0, 1) by the order statistics of a random sample of size n-1 from the uniform distribution U(0,1), for each n. A new integral transformation that is similar to generalized Stieltjes transform is given with various properties. The result of Soltani and Roozegar [On distribution of randomly ordered uniform incremental weighted averages: Divided difference approach. Statist Probab Lett. 2012, 82(5):1012-1020] with this new transform and also integral representation of the Gauss-h…

Beta分布的Bernstein型界

Bernstein-Type Bounds for Beta Distribution

本文为Beta分布建立了尖锐的Bernstein型指数集中不等式，通过由超几何表示导出的二阶中心矩递推改进已有次高斯和次伽马界。

实赋范可除代数下的矩阵广义椭圆二项式级数与中心矩阵变量beta分布

Matrix generalized elliptical binomial series under real normed division algebras and the central matrix variate beta distribution

该研究在椭圆轮廓模型与实赋范可除代数下拓展标量二项式级数至矩阵形式，重新阐释Jack多项式经典超几何级数，还得到可统一推导多类数域下中心矩阵变量II型beta分布的推论。