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Physical Sciences and Mathematics Commons™

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Statistics and Probability

Old Dominion University

1987

Articles 1 - 2 of 2

Full-Text Articles in Physical Sciences and Mathematics

Large Deviation Local Limit Theorems For Ratio Statistics, Sanjeev V. Sabnis Jul 1987

Large Deviation Local Limit Theorems For Ratio Statistics, Sanjeev V. Sabnis

Mathematics & Statistics Theses & Dissertations

Let {T„, n > 1} be an arbitrary sequence of non-lattice random variables and {Sn, n > 1} be another sequence of positive non-lattice random variables. Let the two sequences be independent. Let Ø1n and Ø2n be the moment genereating functions of {Tn, n > 1} and { Sn,n > 1} respectively. Let {an} be a sequence of real numbers such that an —»• oo.

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Limit Theorems In The Area Of Large Deviations For Some Dependent Random Variables, Narasinga Rao Chaganty, Jayaram Sethuraman Jan 1987

Limit Theorems In The Area Of Large Deviations For Some Dependent Random Variables, Narasinga Rao Chaganty, Jayaram Sethuraman

Mathematics & Statistics Faculty Publications

A magnetic body can be considered to consist of n sites, where n is large. The magnetic spins at these n sites, whose sum is the total magnetization present in the body, can be modelled by a triangular array of random variables (X(n) 1,..., X(n) n). Standard theory of physics would dictate that the joint distribution of the spins can be modelled by dQn(x) = zn-1 exp[ -Hn(x)]Π dP(xj), where x = (x1,..., xn) ∈ Rn, where Hn is the Hamiltonian, zn is …

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