Random Discrete Distributions Invariant Under Size - biased Permutation

نویسنده

  • Jim Pitman
چکیده

Invariance of a random discrete distribution under size-biased permutation is equivalent to a conjunction of symmetry conditions on its nite-dimensional distributions. This is applied to characterize residual allocation models with independent factors that are invariant under size-biased permutation. Apart from some exceptional cases and minor modiications, such models form a two-parameter family of generalized Dirichlet distributions.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Characterization of GEM Distributions

Let (X n) be a residual allocation model with i.i.d. residual fractions U n. For a random variable W with values in 0; 1] independent of (X n) we deene another sequence (Y n) by setting Under minor regularity assumptions we show that (X n) and (Y n) have the same probability law if and only if this law is a GEM distribution. In this case, the distribution of W and the U n 's is beta (1;) for so...

متن کامل

Partially Exchangeable Random Partitions

A random partition of the positive integers is called partially exchangeable if for each finite sequence of positive integers n,, ... , nk, the probability that the partition breaks the first n1 + + nk integers into k particular classes, of sizes nl,.. . ., nk in order of their first elements, has the same value p(nl,...,nk) for every possible choice of classes subject to the sizes constraint. ...

متن کامل

Applications of size biased couplings for concentration of measures

Let Y be a nonnegative random variable with mean μ and finite positive variance σ, and let Y , defined on the same space as Y , have the Y size biased distribution, that is, the distribution characterized by E[Y f(Y )] = μEf(Y ) for all functions f for which these expectations exist. Under a variety of conditions on the coupling of Y and Y , including combinations of boundedness and monotonicit...

متن کامل

Sampling formulae arising from random Dirichlet populations

Consider the random Dirichlet partition of the interval into n fragments at temperature θ > 0. Some statistical features of this random discrete distribution are recalled, together with explicit results on the law of its size-biased permutation. Using these, pre-asymptotic versions of the Ewens and Donnelly-Tavaré-Griffiths sampling formulae from finite Dirichlet partitions are computed exactly...

متن کامل

Cycles of Random Permutations with Restricted Cycle Lengths

We prove some general results about the asymptotics of the distribution of the number of cycles of given length of a random permutation whose distribution is invariant under conjugation. These results were first established to be applied in a forthcoming paper [BG], where we prove results about cycles of random permutations which can be written as free words in several independent random permut...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1995