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166
Estimating a tail exponent by modelling departure from a Pareto distribution
- Annals Statist
, 1999
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 53 (1 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
The Peaks over Thresholds Method for Estimating High Quantiles of Loss Distributions
- PROCEEDINGS OF XXVIITH INTERNATIONAL ASTIN COLLOQUIUM
, 1997
"... We review the peaks over thresholds or POT method for modelling tails of loss severity distributions and discuss the use of this technique for estimating high quantiles and the possible relevance of this to excess of loss insurance in high layers. We test the method on a variety of simulated heavy-t ..."
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Cited by 45 (2 self)
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We review the peaks over thresholds or POT method for modelling tails of loss severity distributions and discuss the use of this technique for estimating high quantiles and the possible relevance of this to excess of loss insurance in high layers. We test the method on a variety of simulated heavy-tailed distributions to show what kind of thresholds are required and what sample sizes are necessary to give accurate estimates of quantiles.
Sciences Discussions
, 2007
"... Papers published in Hydrology and Earth System Sciences Discussions are under open-access review for the journal Hydrology and Earth System Sciences Participatory scenario development for integrated assessment of nutrient flows in a Catalan river catchment ..."
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Cited by 40 (3 self)
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Papers published in Hydrology and Earth System Sciences Discussions are under open-access review for the journal Hydrology and Earth System Sciences Participatory scenario development for integrated assessment of nutrient flows in a Catalan river catchment
Statistical Blockade: A Novel Method for Very Fast Monte Carlo Simulation of Rare Circuit Events
- and Its Application,’’ Proc. Design, Automation and Test in Europe Conf. (DATE 07), IEEE CS
, 2007
"... Circuit reliability under statistical process variation is an area of growing concern. For highly replicated circuits such as SRAMs and flip flops, a rare statistical event for one circuit may induce a not-so-rare system failure. Existing techniques perform poorly when tasked to generate both effici ..."
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Cited by 25 (3 self)
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Circuit reliability under statistical process variation is an area of growing concern. For highly replicated circuits such as SRAMs and flip flops, a rare statistical event for one circuit may induce a not-so-rare system failure. Existing techniques perform poorly when tasked to generate both efficient sampling and sound statistics for these rare events. Statistical Blockade is a novel Monte Carlo technique that al-lows us to efficiently filter—to block—unwanted samples insuffi-ciently rare in the tail distributions we seek. The method synthesizes ideas from data mining and Extreme Value Theory, and shows speed-ups of 10X-100X over standard Monte Carlo. 1.
Modeling river flows with heavy tails
- Water Resour. Res
, 1998
"... Abstract. Recent advances in time series analysis provide alternative models for river flows in which the innovations have heavy tails, so that some of the moments do not exist. The probability of large fluctuations is much larger than for standard models. We survey some recent theoretical developme ..."
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Cited by 24 (8 self)
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Abstract. Recent advances in time series analysis provide alternative models for river flows in which the innovations have heavy tails, so that some of the moments do not exist. The probability of large fluctuations is much larger than for standard models. We survey some recent theoretical developments for heavy tail time series models and illustrate their practical application to river flow data from the Salt River near Roosevelt, Arizona. We also include some simple diagnostics that the practitioner can use to identify when the methods of this paper may be useful. 1.
High volatility, thick tails and extreme value theory in value-at-risk estimation
- Insurance: Mathematics and Economics
, 2003
"... In this paper, the performance of the extreme value theory in Value-at-Risk calculations is compared to the performances of other well-known modeling techniques, such as GARCH, variance-covariance method and historical simulation in a volatile stock market. The models studied can be classified into ..."
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Cited by 23 (2 self)
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In this paper, the performance of the extreme value theory in Value-at-Risk calculations is compared to the performances of other well-known modeling techniques, such as GARCH, variance-covariance method and historical simulation in a volatile stock market. The models studied can be classified into two groups. The first group consists of GARCH(1,1) and GARCH(1,1)-t models which yield highly volatile quantile forecasts. The other group, consisting of historical simulation, variance-covariance approach, adaptive generalized pareto distribution (GPD) and nonadaptive GPD models leads to more stable quantile forecasts. The quantile forecasts of GARCH(1,1) models are excessively volatilite relative to the GPD quantile forecasts. This makes the GPD model to be a robust quantile forecasting tool which is practical to implement and regulate for VaR measurements. Key Words: Value-at-Risk, financial risk management, extreme value theory.
Parameter Estimation for the Truncated Pareto Distribution
- Journal of the American Statistical Assoc
, 2006
"... The Pareto distribution is a simple model for nonnegative data with a power law probability tail. In many practical applications, there is a natural upper bound that truncates the prob-ability tail. This paper derives estimators for the truncated Pareto distribution, investigates their properties, a ..."
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Cited by 22 (4 self)
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The Pareto distribution is a simple model for nonnegative data with a power law probability tail. In many practical applications, there is a natural upper bound that truncates the prob-ability tail. This paper derives estimators for the truncated Pareto distribution, investigates their properties, and illustrates a way to check for fit. We illustrate these methods with applications from finance, hydrology and atmospheric science.
Fractional Dispersion, Lévy Motion, and the MADE Tracer Tests
- Transp. Por. Media
, 1999
"... The macrodispersion experiments (MADE) at the Columbus Air Force Base in Mississippi were conducted in a highly heterogeneous aquifer that violates the basic assumptions of local 2 -- order theories. A governing equation that describes particles that undergo Lvy motion, rather than Brownian motio ..."
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Cited by 21 (15 self)
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The macrodispersion experiments (MADE) at the Columbus Air Force Base in Mississippi were conducted in a highly heterogeneous aquifer that violates the basic assumptions of local 2 -- order theories. A governing equation that describes particles that undergo Lvy motion, rather than Brownian motion, readily describes the highly skewed and heavy--tailed plume development at the MADE site. The new governing equation is based on a fractional, rather than integer, order of differentiation. This order (#), based on MADE plume measurements, is approximately 1.1. The hydraulic conductivity (K) increments also follow a power law of order # = 1.1. We conjecture that the heavy--tailed K distribution gives rise to a heavy--tailed velocity field that directly implies the fractional--order governing equation derived herein. Simple arguments lead to accurate estimates of the velocity and dispersion constants based only on the aquifer hydraulic properties. This supports the idea that the correct governing equation can be accurately determined before, or after, a contamination event. While the traditional ADE fails to model a conservative tracer in the MADE aquifer, the fractional equation predicts tritium concentration profiles with remarkable accuracy over all spatial and temporal scales.
