Abstract
In this article, skew-elliptical time series are defined in order to account for both skewness and kurtosis, with particular emphasis on the skew-normal and skew-t distributions. The bivariate skew-t distribution is then used to describe a 63 year time series of hourly sea levels measured at Charlottetown, Atlantic Canada. It is shown that the skew-t fits the data better than the normal distribution and it can be used to recover return periods of extreme levels based on a standard analysis of 63 annual maxima. Preliminary results are presented to show how the skew-t distribution may be used to estimate changes in flooding risk resulting from changes in sea level rise, storminess, and other climatic factors.
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References
A. Azzalini, A class of distributions which includes the normal ones, Scand. J. Stat., 12 (1985), pp. 171–178.
A. Azzalini and A. Dalla Valle, The multivariate skew-normal distribution, Biometrika, 83 (1996), pp. 715–726.
A. Azzalini and A. Capitanio, Statistical applications of the multivariate skew normal distribution, J. R. Statist. Soc., B 61 (1999), pp. 579–602.
M.D. Branco and D.K. Dey, A generalclass of multivariate skew-elliptical distributions, Journal of Multivariate Analysis, 79 (2001), pp. 99–113.
M.G. Genton, L. He, and X. Liu, Moments of skew-normal random vectors and their quadratic forms, Statistics and Probability Letters, 51 (2001), pp. 319–325.
M.G. Genton and N.M. Loperfido, Generalized skew-elliptical distributions and their quadratic forms (2002), Institute of Statistics Mimeo - Series #2539, under review.
D.C. Hoaglin, F. Mosteller and J.W. Tukey, Exploring Data Tables, Trends, and Shapes, Wiley, 1985.
M.R. Leadbetter, G. Lindgren, and H. Rootzen, Extremes and Related Properties of Random Sequences and Processes, Springer Series in Statistics, Springer-Verlag, 1982.
D.T. Pugh and I.M. Vassie, Applications of the Joint Probability Method for Extreme Sea Level Computations, Proceedings of the Institute of Civil Engineers, Part 2, 69, 959–975, 1980.
S.K. Sahu, D.K. Dey, and M.D. Branco, A new class of multivariate skew distributions with applications to Bayesian regression models, The Canadian Journal of Statistics, 31 (2003).
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© 2004 Springer-Verlag New York, LLC
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Genton, M.G., Thompson, K.R. (2004). Skew-Elliptical Time Series with Application to Flooding Risk. In: Brillinger, D.R., Robinson, E.A., Schoenberg, F.P. (eds) Time Series Analysis and Applications to Geophysical Systems. The IMA Volumes in Mathematics and its Applications, vol 139. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9386-3_9
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DOI: https://doi.org/10.1007/978-1-4684-9386-3_9
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