Statistical Analysis of Extreme Values

Reiss, Rolf–Dieter; Thomas, Michael E.

doi:10.1007/978-3-0348-6336-0

Cited by 329 publications

(302 citation statements)

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“…The tail-shape parameter can be estimated using the methods of Reiss and Thomas (1997), who fit observed maxima to the three extreme-value distributions, just as we did for Drug A's excipient and formulation in the Inhale example. Another approach would be to simulate data on the potential profit outcomes from the underlying profit distribution, H x , as we did for Drug C's device in the Inhale example.…”

Section: Resultsmentioning

confidence: 99%

An Extreme-Value Model of Concept Testing

2001

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W e model concept testing in new product development as a search for the most profitable solution to a design problem. When allocating resources, developers must balance the cost of testing multiple designs against the potential profits that may result. We propose extreme-value theory as a mathematical abstraction of the concept-testing process. We investigate the trade-off between the benefits and costs of parallel concept testing and derive closed-form solutions for the case of profits that follow extreme-value distributions. We analyze the roles of the scale and tail-shape parameters of the profit distribution as well as the cost of testing in determining the optimal number of tests and total budget for the concept phase of NPD. Using an example, we illustrate how to estimate and interpret the scale and tail-shape parameters. We find that the impact of declining concept-testing costs on expected profits, the number of concepts tested, and total spending depend on the scale/cost ratio and tail-shape parameter of the profit distribution.

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Section: Resultsmentioning

confidence: 99%

An Extreme-Value Model of Concept Testing

2001

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“…We outline the fundamental aspects of each method. Further details can be found in Embrechts, Klüppelberg and Mikosch (1997) and Reiss and Thomas (1997).…”

Section: Univariate Methodsmentioning

confidence: 99%

Modelling Extreme-Value Dependence in International Stock Markets

2002

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In the finance literature, cross-sectional dependence in extreme returns of risky assets is often modelled implicitly assuming an asymptotically dependent structure. If the true dependence structure is asymptotically independent then current modelling approaches will lead to an over-estimation of the risk of simultaneous extreme events. We use two simple nonparametric measures to identify and quantify the tail dependence among stock returns in five international stock markets. We show that there is strong evidence in favour of asymptotically independent models for the tail structure of stock market returns, and that most of the extremal dependence is due to heteroskedasticity in stock returns processes. Using a range of volatility filters, we find that tail index and tail dependence can be partially captured by models for heteroskedasticity. We find there is no clear reason to prefer one volatility filter over another.

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“…These two extremes were determined to result from unusual natural conditions and as such were addressed by Pima County in a Natural Events Action Plan (NEAP). The underlying ξ for the ozone tail is −0.24, indicating a beta (bounded tail) distribution, while PM has ξ equal to +0.12, a Pareto (heavy tail) distribution (Reiss and Thomas, 2001).…”

Section: Observed Extremesmentioning

confidence: 99%

Climate‐based sensitivity of air quality to climate change scenarios for the southwestern United States

Wise

2008

Intl Journal of Climatology

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ABSTRACT:The need to understand future trends in air quality is an issue that is frequently raised by air quality planners and managers. The potential for extreme events is of particular interest, but forecasts are difficult using traditional methods and further complicated by predictions of future climate change. This study aims to address this research need through a climate-based sensitivity study of ground-level ozone and particulate matter (PM) in the U.S. Southwest. Extreme value methods were used to examine ozone and PM in Tucson, Arizona, over the time period 1990-2001. A Statistical DownScaling Model (SDSM) was employed to build regression-based models between gridded meteorological data and point time series of ozone and PM. Following model calibration and verification, future climate-based ozone and PM scenarios were created for 2002-2050 and 2051-2099. Daily output of projected ozone and PM were then subjected to extreme value methods in order to estimate climate-based changes in ozone and PM extremes over the next century. Results indicate that monthly mean and extreme ozone values are sensitive to predicted increases in temperature, particularly in the summer months. PM results are less certain but suggest that PM may be sensitive to changing moisture conditions.

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Statistical Analysis of Extreme Values

Cited by 329 publications

References 0 publications

An Extreme-Value Model of Concept Testing

An Extreme-Value Model of Concept Testing

Modelling Extreme-Value Dependence in International Stock Markets

Climate‐based sensitivity of air quality to climate change scenarios for the southwestern United States

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