Modeling of Infinite Divisible Distributions Using Invariant and Equivariant Functions
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Abstract: (4257 Views) |
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 to Basu’s theorem, this application requires a version of the Goldie-Steutel law. By using Basu’s theorem that a large class of functions of random variables, two of which are independent standard normal, is infinitely divisible. The next result provides a representation of functions of normal variables as the product of two random variables, where one is infinitely divisible, while the other is not, and the two are independently distributed.
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Keywords: infinite divisible distributions, goldie-Steutel law, scale equivariant function, scale invariant function. |
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Full-Text [PDF 274 kb]
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Type of Study: Research |
Subject:
Special Received: 2015/05/4 | Accepted: 2016/11/20 | Published: 2016/11/20
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