Advances and Applications in Statistics
Volume 20, Issue 2, Pages 89 - 99
(February 2011)
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EXCEEDANCE MEASURE OF AMPLIFIED AND DE-AMPLIFIED CLASSES OF ALGEBRAIC POLYNOMIALS
K. Farahmand and Jianliang Gao
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Abstract: There are many articles that aim at detecting the mathematical behavior of polynomials with random coefficients. They are initiated from classical algebraic polynomials ?Later an interest got developed by physicists and mathematicians to study polynomials which include binomial elements. Here we introduce several new forms of polynomials, with binomial elements and show how the behavior of polynomials changes with additional terms in coefficients. We present the results in order to better understand the behavior of polynomials by looking first at the properties of the expected number of zeros, as this represents the number of oscillations of polynomials, as well as the expected exceedance measure which gives the area under the curve. The distribution of the coefficients is assumed to be normal. |
Keywords and phrases: number of real zeros, real roots, random algebraic polynomials, Kac-Rice formula, exceedance measure. |
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