Omega function: a theoretical introduction

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2009
Authors
Nguyen, Vu Ngoc
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Ramsey, Thomas
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University of Hawaii at Manoa
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This paper investigates the theory behind a new universal performance measure (the so called Omega function), which was frst introduced by Con Keating and William F. Shadwick in 2002 (see [1]). In the frst section, we review some rudimentary probability. We then defne the Omega function, introduce some of its properties, and prove these properties without continuity assumptions. We also defne the standard dispersion, a new statistic derived from the Omega function. We prove one new theorem about the range of the standard dispersion for a fnite sample. The structure of the second section on the Omega function follows closely that of a recent talk given by Ana Cascon and William Shadwick in [4]. In the last section, we demonstrate these properties with real-life data.
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Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2009
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28 pages
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