Distribution of a Random Functional of a Ferguson- Dirichlet Process over the Unit Sphere
نویسنده
چکیده
Jiang, Dickey, and Kuo [12] gave the multivariate c-characteristic function and showed that it has properties similar to those of the multivariate Fourier transformation. We first give the multivariate c-characteristic function of a random functional of a Ferguson-Dirichlet process over the unit sphere. We then find out its probability density function using properties of the multivariate c-characteristic function. This new result would generalize that given by [11].
منابع مشابه
Introducing of Dirichlet process prior in the Nonparametric Bayesian models frame work
Statistical models are utilized to learn about the mechanism that the data are generating from it. Often it is assumed that the random variables y_i,i=1,…,n ,are samples from the probability distribution F which is belong to a parametric distributions class. However, in practice, a parametric model may be inappropriate to describe the data. In this settings, the parametric assumption could be r...
متن کاملA Hierarchial Dirichlet Process Prior
By taking the governing measure of a Dirichlet process as essentially the realization of a Dirichlet process itself, a hierarchical Dirichlet process emerges. This distribution enables the Bayesian treatment of two level hierarchical random effects models, with results paralleling those of Ferguson (1973).
متن کاملDirichlet Random Walks
This paper provides tools for the study of the Dirichlet random walk in R . We compute explicitly, for a number of cases, the distribution of the random variableW using a form of Stieltjes transform ofW instead of the Laplace transform, replacing the Bessel functions with hypergeometric functions. This enables us to simplify some existing results, in particular, some of the proofs by Le Caër (2...
متن کاملOptimal Batch Production for a Single Machine System with Accumulated Defectives and Random Rate of Rework
In this paper we consider an imperfect production system which produces good and defective items and assume that defective items can be reworked. Due to the nature of rework process we do not restrict the rework rate to be equal to normal production rate or constant and assume that it is a random variable with an arbitrary distribution function. We also assume as it is true in most real world s...
متن کاملMoments and Cumulants in Infinite Dimensions with Applications to Poisson, Gamma and Dirichlet–ferguson Random
We show that the chaos representation of some Compound Poisson Type processes displays an underlying intrinsic combinatorial structure, partly independent of the chosen process. From the computational viewpoint, we solve the arising combinatorial complexity by means of the moments/cumulants duality for the laws of the corresponding processes, themselves measures on distributional spaces, and pr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008