Abstract
In this paper experimental designs are considered for classic extreme value distribution models. A careful review of the literature provides some information matrices in order to study experimental designs. Regression models and their design implications are discussed for some situations involving extreme values. These include a constant variance and a constant coefficient of variation model plus an application in the context of strength of materials. Relative efficiencies calculated with respect to D-optimality are used to compare the designs given in this example.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aitchison J, Brown J (1957) The Lognormal Distribution. CUP, Cambridge
Atkinson A, Donev A (1992) Optimum Experimental Designs. Oxford Science Publications, Oxford
Bailey RA (1982) The decomposition of treatment degrees of freedom in quantitative factorial experiments. J Roy Stat Soc, B 44:63–70
Coles S (2001) An Introduction to Statistical Modeling of Extreme Values Series. Springer, New York
Fedorov V, P H (1997) Model-Oriented Design of Experiments. Springer, New York
Finley HF (1967) An extreme value statistical analysis of maximum pit depths and time to first perforation. Corrosion 23:83–87
Fisher RA, Tippett LHC (1982) Limiting forms of the frequency distributions of the largest or smallest member of a sample. Proc Camb Phil Soc 24:180–190
Ford I, Torsney B, Wu C (1992) The use of a canonical form in the construction of locally optimal designs for non-linear problems. J Roy Stat Soc, B 54:569–583
Gumbel E (1958) Statistics of Extremes. Columbia University Press, New York
Jenkinson AF (1955) The frequency distribution of the annual maximum (or minimum) values of meteorological elements. Quart J Roy Met Soc 81:158–165
Kendall M, Stuart A (1976) The Advanced Theory of Statistics, Vol 3, Design and Analysis and Time Series. Hafner, 3rd edn., New York
Laycock P, Cottis R, Scarf P (1990) Extrapolation of extreme pit depths in space and time. J Electrochem Soc 137:64–69
Leadbetter M, Lindgren G, Rootzen H (1983) Extremes and Related Properties of Random Sequences and Processes. Springer, New York
McCullagh P, Nelder J (1989) Generalized Linear Models. Chapman and Hall, 2nd edn., London
Reiss RD, Thomas M (1997) Statistical Analysis of Extreme Values. Birkhauser Verlag, Basel
Scarf P, Laycock P, Cottis R (1992) Extrapolation of extreme pit depths in space and time, using the r deepest depths. J Electrochem Soc 139:2621–2627
Silvey S (1980) Optimal design. Chapman and Hall, London
Walden A, Prescott P, Webber N (1981) Some important considerations in the analysis of annual maximum sea levels. Coastal Engineering 4:335–342
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Physica-Verlag Heidelberg
About this paper
Cite this paper
Laycock, P.J., López-Fidalgo, J. (2007). Design of Experiments for Extreme Value Distributions. In: López-Fidalgo, J., Rodríguez-Díaz, J.M., Torsney, B. (eds) mODa 8 - Advances in Model-Oriented Design and Analysis. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-1952-6_13
Download citation
DOI: https://doi.org/10.1007/978-3-7908-1952-6_13
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-1951-9
Online ISBN: 978-3-7908-1952-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)