37,784 research outputs found
Probability distribution theory, generalisations and applications of l-moments
In this thesis, we have studied L-moments and trimmed L-moments (TL-moments) which are both linear functions of order statistics. We have derived expressions for exact variances and covariances of sample L-moments and of sample TL-moments for any sample size n in terms of first and second-order moments of order statistics from small conceptual sample sizes, which do not depend on the actual sample size n. Moreover, we have established a theorem which characterises the normal distribution in terms of these second-order moments and the characterisation suggests a new test of normality. We have also derived a method of estimation based on TL-moments which gives zero weight to extreme observations. TL-moments have certain advantages over L-moments and method of moments. They exist whether or not the mean exists (for example the Cauchy distribution) and they are more robust to the presence of outliers. Also, we have investigated four methods for estimating the parameters of a symmetric lambda distribution: maximum likelihood method in the case of one parameter and L-moments, LQ-moments and TL-moments in the case of three parameters. The L-moments and TL-moments estimators are in closed form and simple to use, while numerical methods are required for the other two methods, maximum likelihood and LQ-moments. Because of the flexibility and the simplicity of the lambda distribution, it is useful in fitting data when, as is often the case, the underlying distribution is unknown. Also, we have studied the symmetric plotting position for quantile plot assuming a symmetric lambda distribution and conclude that the choice of the plotting position parameter depends upon the shape of the distribution. Finally, we propose exponentially weighted moving average (EWMA) control charts to monitor the process mean and dispersion using the sample L-mean and sample L-scale and charts based on trimmed versions of the same statistics. The proposed control charts limits are less influenced by extreme observations than classical EWMA control charts, and lead to tighter limits in the presence of out-of-control observations
Robust estimation and inference for heavy tailed GARCH
We develop two new estimators for a general class of stationary GARCH models
with possibly heavy tailed asymmetrically distributed errors, covering
processes with symmetric and asymmetric feedback like GARCH, Asymmetric GARCH,
VGARCH and Quadratic GARCH. The first estimator arises from negligibly trimming
QML criterion equations according to error extremes. The second imbeds
negligibly transformed errors into QML score equations for a Method of Moments
estimator. In this case, we exploit a sub-class of redescending transforms that
includes tail-trimming and functions popular in the robust estimation
literature, and we re-center the transformed errors to minimize small sample
bias. The negligible transforms allow both identification of the true parameter
and asymptotic normality. We present a consistent estimator of the covariance
matrix that permits classic inference without knowledge of the rate of
convergence. A simulation study shows both of our estimators trump existing
ones for sharpness and approximate normality including QML, Log-LAD, and two
types of non-Gaussian QML (Laplace and Power-Law). Finally, we apply the
tail-trimmed QML estimator to financial data.Comment: Published at http://dx.doi.org/10.3150/14-BEJ616 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Gravitation Physics at BGPL
We report progress on a program of gravitational physics experiments using
cryogenic torsion pendula undergoing large-amplitude torsion oscillation. This
program includes tests of the gravitational inverse square law and of the weak
equivalence principle. Here we describe our ongoing search for
inverse-square-law violation at a strength down to of standard
gravity. The low-vibration environment provided by the Battelle Gravitation
Physics Laboratory (BGPL) is uniquely suited to this study.Comment: To be published in The Proceedings of the Francesco Melchiorri
Memorial Conference as a special issue of New Astronomy Review
Cram\'{e}r type large deviations for trimmed L-statistics
In this paper, we propose a new approach to the investigation of asymptotic
properties of trimmed -statistics and we apply it to the Cram\'{e}r type
large deviation problem. Our results can be compared with ones in Callaert et
al.(1982) -- the first and, as far as we know, the single article, where some
results on probabilities of large deviations for the trimmed -statistics
were obtained, but under some strict and unnatural conditions. Our approach is
to approximate the trimmed -statistic by a non-trimmed -statistic (with
smooth weight function) based on Winsorized random variables. Using this
method, we establish the Cram\'{e}r type large deviation results for the
trimmed -statistics under quite mild and natural conditions.Comment: 17 page
Coupled flight dynamics and CFD - demonstration for helicopters in shipborne environment
The development of high-performance computing and computational fluid dynamics methods have evolved to the point where it is possible to simulate complete helicopter configurations with good accuracy. Computational fluid dynamics methods have also been applied to problems such as rotor/fuselage and main/tail rotor interactions, performance studies in hover and forward flight, rotor design, and so on. The GOAHEAD project is a good example of a coordinated effort to validate computational fluid dynamics for complex helicopter configurations. Nevertheless, current efforts are limited to steady flight and focus mainly on expanding the edges of the flight envelope. The present work tackles the problem of simulating manoeuvring flight in a computational fluid dynamics environment by integrating a moving grid method and the helicopter flight mechanics solver with computational fluid dynamics. After a discussion of previous works carried out on the subject and a description of the methods used, validation of the computational fluid dynamics for ship airwake flow and rotorcraft flight at low advance ratio are presented. Finally, the results obtained for manoeuvring flight cases are presented and discussed
Laboratory Tests of Gravitational Physics Using a Cryogenic Torsion Pendulum
Progress and plans are reported for a program of gravitational physics
experiments using cryogenic torsion pendula undergoing large amplitude
torsional oscillation. The program includes a UC Irvine project to measure the
gravitational constant G and joint UC Irvine - U. Washington projects to test
the gravitational inverse square law at a range of about 10 cm and to test the
weak equivalence principle.Comment: 17 pages, 11 figures, contribution to the 10th Marcel Grossman
Conference Proceedings (Rio de Janeiro, July 20 - 26, 2003) - changed wording
in first paragraph of section
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