scholarly journals Reply

2011 ◽  
Vol 50 (1) ◽  
pp. 267-270 ◽  
Author(s):  
Lasse Makkonen
Keyword(s):  
Order Statistics ◽  
Sampling Error ◽  
Extreme Weather ◽  
Extreme Value ◽  
Extreme Weather Events ◽  
Extreme Value Analysis ◽  
Exact Probability ◽  
Value Analysis ◽  
Weather Events

Abstract This reply addresses the use of order statistics in extreme value analysis. The author has previously proposed in this journal that the distribution-dependent estimators of plotting position in extreme value analysis should be abandoned and replaced by the Weibull formula. It was also demonstrated that the use of the wrong plotting positions has resulted in underestimation of the probability of extreme-weather events. Cook’s comments challenge these developments and defend the previously presented plotting methods. In this reply it is outlined that the Weibull formula provides the exact probability PI of nonexceedance in order-ranked data. Hence, there is no sampling error related to PI. This renders Cook’s primary arguments invalid. The specific critical comments by Cook are also replied to and are shown to be unfounded.

scholarly journals EXTREME VALUE ANALYSIS WITHOUT THE LARGEST VALUES: WHAT CAN BE DONE?

2019 ◽  
Vol 34 (2) ◽  
pp. 200-220
Author(s):  
Jingjing Zou ◽  
Richard A. Davis ◽  
Gennady Samorodnitsky
Keyword(s):  
Order Statistics ◽  
Extreme Values ◽  
Sample Path ◽  
Estimation Procedure ◽  
Extreme Value ◽  
Hill Estimator ◽  
Extreme Value Analysis ◽  
Value Analysis ◽  
Heavy Tailed ◽  
The Hill

AbstractIn this paper, we are concerned with the analysis of heavy-tailed data when a portion of the extreme values is unavailable. This research was motivated by an analysis of the degree distributions in a large social network. The degree distributions of such networks tend to have power law behavior in the tails. We focus on the Hill estimator, which plays a starring role in heavy-tailed modeling. The Hill estimator for these data exhibited a smooth and increasing “sample path” as a function of the number of upper order statistics used in constructing the estimator. This behavior became more apparent as we artificially removed more of the upper order statistics. Building on this observation we introduce a new version of the Hill estimator. It is a function of the number of the upper order statistics used in the estimation, but also depends on the number of unavailable extreme values. We establish functional convergence of the normalized Hill estimator to a Gaussian process. An estimation procedure is developed based on the limit theory to estimate the number of missing extremes and extreme value parameters including the tail index and the bias of Hill's estimator. We illustrate how this approach works in both simulations and real data examples.

scholarly journals Comments on “Plotting Positions in Extreme Value Analysis”

2011 ◽  
Vol 50 (1) ◽  
pp. 255-266 ◽  
Author(s):  
Nicholas Cook
Keyword(s):  
Sampling Error ◽  
Extreme Value ◽  
Building Codes ◽  
Extreme Value Analysis ◽  
Model Parameters ◽  
Value Analysis ◽  
Opposite Case ◽  
Past Half Century ◽  
Unique Status

Abstract This comment addresses the role of sampling error in extreme value analysis. A note published in this journal claimed that Weibull’s 1939 estimator for sample probability has a unique status that invalidates all other estimators and renders invalid all of the developments of unbiased distribution-dependent estimators made since 1939. The note concluded that the use of distribution-dependent estimators should be abandoned and that many estimates of the weather-related risks should be reevaluated and the related building codes and other related regulations updated. This comment uses rigorous statistical proofs to make the diametrically opposite case: namely, that development of distribution-dependent estimators has resulted in an improvement in accuracy over the past half century and that no changes are required to the basis of weather-related building codes and regulations. These rigorous proofs are supplemented by sampling experiments that demonstrate their validity. This comment provides an introduction to the basic statistical concepts of the statistical modeling of extremes, including unbiased estimators for the model parameters.

scholarly journals Extreme weather events and high Colombian food prices: A non-stationary extreme value approach

2021 ◽  
Author(s):  
Luis Fernando Melo-Velandia ◽  
Camilo Andrés Orozco-Vanegas ◽  
Daniel Parra-Amado
Keyword(s):  
Weather Conditions ◽  
Extreme Weather ◽  
Extreme Value ◽  
Food Prices ◽  
Extreme Weather Events ◽  
Processed Foods ◽  
Fuel Prices ◽  
Weather Events ◽  
High Precipitation ◽  
Extreme Value Model

Given the importance of climate change and the increase of its severity under extreme weather events, we analyze the main drivers of high food prices in Colombia between 1985 and 2020 focusing on extreme weather shocks like a strong El Ni˜no.We estimate a non-stationary extreme value model for Colombian food prices. Our findings suggest that perishable foods are more exposed to extreme weather conditions in comparison to processed foods. In fact, an extremely low precipitation level explains only high prices in perishable foods. The risk of high perishable food prices is significantly larger for low rainfall levels (dry seasons) compared to high precipitation levels (rainy seasons). This risk gradually results in higher perishable food prices. It is non linear and is also significantly larger than the risk related to changes in the US dollar-Colombian peso exchange rate and fuel prices. Those covariates also explain high prices for both perishable and processed foods. Finally, we find that the events associated with the strongest El Ni˜no in 1988 and 2016 are expected to reoccur once every 50 years.

scholarly journals Plotting Positions in Extreme Value Analysis

2006 ◽  
Vol 45 (2) ◽  
pp. 334-340 ◽  
Author(s):  
Lasse Makkonen
Keyword(s):  
Extreme Events ◽  
Standard Technique ◽  
Extreme Weather Events ◽  
Extreme Value Analysis ◽  
Cumulative Probability ◽  
Return Periods ◽  
Value Analysis ◽  
Probability Paper ◽  
Weather Events ◽  
Order Of Magnitude

Abstract Plotting order-ranked data is a standard technique that is used in estimating the probability of extreme weather events. Typically, observations, say, annual extremes of a period of N years, are ranked in order of magnitude and plotted on probability paper. Some statistical model is then fitted to the order-ranked data by which the return periods of specific extreme events are estimated. A key question in this method is as follows: What is the cumulative probability P that should be associated with the sample of rank m? This issue of the so-called plotting positions has been debated for almost a century, and a number of plotting rules and computational methods have been proposed. Here, it is shown that in estimating the return periods there is only one correct plotting position: P = m/(N + 1). This formula predicts much shorter return periods of extreme events than the other commonly used methods. Thus, many estimates of the weather-related risks should be reevaluated and the related building codes and other related regulations updated.

Modeling European hot spells using extreme value analysis

2014 ◽  
Vol 58 (3) ◽  
pp. 193-207 ◽  
Author(s):  
C Photiadou ◽  
MR Jones ◽  
D Keellings ◽  
CF Dewes
Keyword(s):  
Extreme Value ◽  
Extreme Value Analysis ◽  
Value Analysis ◽  
Hot Spells

Reliability, Resilience and the Oncoming Wave of Retiring Baseload Units, Volume I: The Critical Role of Thermal Units During Extreme Weather Events

2018 ◽  
Author(s):  
Peter C. Balash, PhD ◽  
Kenneth C. Kern ◽  
John Brewer ◽  
Justin Adder ◽  
Christopher Nichols ◽  
...  
Keyword(s):  
Critical Role ◽  
Extreme Weather ◽  
Extreme Weather Events ◽  
Weather Events
Sign in / Sign up

Export Citation Format

Share Document