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Some Bounds on the Distribution of Certain Quadratic Forms in Normal Random Variables

✍ Scribed by Hongsheng Gao; Peter Smith

Book ID
108521372
Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
75 KB
Volume
40
Category
Article
ISSN
1369-1473

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πŸ“œ SIMILAR VOLUMES

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A general distribution which will be called the noncentral generalized Laplacian (NGL) is introduced and its properties studied. Then a set of results are obtained which will give the necessary and sufficient conditions for a bilinear expression or a quadratic expression to be distributed as a NGL.

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Let {Z i , i β‰₯ 1} be a linear process defined by Z t = ∞ j=0 d j ΞΎ t-j with {d j , j β‰₯ 0} being a regular varying sequence of real numbers and {ΞΎ t , -∞ < t < ∞} being a sequence of Ο†-mixing random variables. The present paper studies the asymptotic behavior of the quadratic form n k,l=1 Β΅(kl)Z k Z