Multivariate Elliptical Truncated Moments

In this study, we derive analytic expressions for the elliptical truncated moment generating function (MGF), the zeroth-, first-, and second-order moments of quadratic forms of the multivariate normal, Student’s , and generalized hyperbolic distributions. The resulting formulas were tested in a numerical application to calculate an analytic expression of the expected shortfall of quadratic portfolios with the benefit that moment based sensitivity measures can be derived from the analytic expression. The convergence rate of the analytic expression is fast–one iteration–for small closed integration domains, and slower for open integration domains when compared to the Monte Carlo integration method. The analytic formulas provide a theoretical framework for calculations in robust estimation, robust regression, outlier detection, design of experiments, and stochastic extensions of deterministic elliptical curves results

An Analysis Of Flow Behavior From A Gas Turbine Combustor Using A Laser Doppler Velcimeter

The purpose of this research was to analyze the flow behavior of air through a combustor and pilot assembly. The combustor was designed to support a combustion flame in gas turbine, and the pilot was the apparatus by which fuel would be supplied to the flame. This research was performed at the University of Central Florida main campus in Orlando, Fl., and was sponsored by Siemens-Westinghouse Power Corporation (SWPC). The combustor and pilot were supplied by SWPC for the purpose of characterizing the flow behavior through them. The focus of the research was to determine the axial and tangential velocity components of the flow. Both components were present due to the fact that the assembly was designed to produce a swirled flow, resulting in a recirculation zone. The main goal of the research conducted was to aid in the combustor design process of SWPC. Measurement of the velocity components was done by using a laser doppler velocimeter (LDV). This research was performed under the supervision of Dr. Ruey-Hung Chen of the Mechanical, Materials, and Aerospace Engineering (MMAE) Department of the University of Central Florida, and will be submitted in partial fulfillment for the Master\u27s Degree in Aerospace Engineering. © 2001 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved