منابع مشابه
Modeling of Infinite Divisible Distributions Using Invariant and Equivariant Functions
Basu’s theorem is one of the most elegant results of classical statistics. Succinctly put, the theorem says: if T is a complete sufficient statistic for a family of probability measures, and V is an ancillary statistic, then T and V are independent. A very novel application of Basu’s theorem appears recently in proving the infinite divisibility of certain statistics. In addition ...
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Given a probability distribution µ a set Λ(µ) of positive real numbers is introduced, so that Λ(µ) measures the " divisibility " of µ. The basic properties of Λ(µ) are described and examples of probability distributions are given, which exhibit the existence of a continuum of situations interpolating the extreme cases of infinitely and minimally divisible probability distributions.
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The infinite divisibility of probability distributions on the space P(R) of probability distributions on R is defined and related fundamental results such as the Lévy-Khintchin formula, representation of Itô type of infinitely divisible RPD, stable RPD and Lévy processes on P(R) are obtained. As an application we investigate limiting behaviors of a simple model of a particle motion in a random ...
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In this paper, we construct the new class of tempered infinitely divisible (TID) distributions. Taking into account the tempered stable distribution class, as introduced by in the seminal work of Rosińsky [10], a modification of the tempering function allows one to obtain suitable properties. In particular, TID distributions may have exponential moments of any order and conserve all proper prop...
متن کاملCharacteristic Kernels and Infinitely Divisible Distributions
We connect shift-invariant characteristic kernels to infinitely divisible distributions on R. Characteristic kernels play an important role in machine learning applications with their kernel means to distinguish any two probability measures. The contribution of this paper is twofold. First, we show, using the Lévy–Khintchine formula, that any shift-invariant kernel given by a bounded, continuou...
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ژورنال
عنوان ژورنال: Forum Mathematicum
سال: 1998
ISSN: 0933-7741,1435-5337
DOI: 10.1515/form.10.6.687