scholarly journals Modeling of Extreme Values via Exponential Normalization Compared with Linear and Power Normalization

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1876
Author(s):  
Haroon Mohamed Barakat ◽  
Osama Mohareb Khaled ◽  
Nourhan Khalil Rakha
Keyword(s):  
Extreme Values ◽  
Real Data ◽  
Extreme Value ◽  
Data Sets ◽  
Power Normalization ◽  
Generalized Pareto ◽  
Extreme Value Theorem ◽  
Generalized Pareto Distributions ◽  
Asymmetric Distributions ◽  
Theoretical Results

Several new asymmetric distributions have arisen naturally in the modeling extreme values are uncovered and elucidated. The present paper deals with the extreme value theorem (EVT) under exponential normalization. An estimate of the shape parameter of the asymmetric generalized value distributions that related to this new extension of the EVT is obtained. Moreover, we develop the mathematical modeling of the extreme values by using this new extension of the EVT. We analyze the extreme values by modeling the occurrence of the exceedances over high thresholds. The natural distributions of such exceedances, new four generalized Pareto families of asymmetric distributions under exponential normalization (GPDEs), are described and their properties revealed. There is an evident symmetry between the new obtained GPDEs and those generalized Pareto distributions arisen from EVT under linear and power normalization. Estimates for the extreme value index of the four GPDEs are obtained. In addition, simulation studies are conducted in order to illustrate and validate the theoretical results. Finally, a comparison study between the different extreme models is done throughout real data sets.

scholarly journals Extreme Value Analysis for Time-variable Mixed Workload

2021 ◽  
Author(s):  
Szilárd Bozóki ◽  
András Pataricza
Keyword(s):  
Extreme Values ◽  
Real Life ◽  
Extreme Value ◽  
Time Variable ◽  
Extreme Value Analysis ◽  
Computing Systems ◽  
Value Analysis ◽  
Root Cause ◽  
Extreme Value Theorem ◽  
Dynamic Time

Proper timeliness is vital for a lot of real-world computing systems. Understanding the phenomena of extreme workloads is essential because unhandled, extreme workloads could cause violation of timeliness requirements, service degradation, and even downtime. Extremity can have multiple roots: (1) service requests can naturally produce extreme workloads; (2) bursts could randomly occur on a probabilistic basis in case of a mixed workload in multiservice systems; (3) workload spikes typically happen in deadline bound tasks.Extreme Value Analysis (EVA) is a statistical method for modeling the extremely deviant values corresponding to the largest values. The foundation mathematics of EVA, the Extreme Value Theorem, requires the dataset to be independent and identically distributed. However, this is not generally true in practice because, usually, real-life processes are a mixture of sources with identifiable patterns. For example, seasonality and periodic fluctuations are regularly occurring patterns. Deadlines can be purely periodic, e.g., monthly tax submissions, or time variable, e.g., university homework submission with variable semester time schedules.We propose to preprocess the data using time series decomposition to separate the stochastic process causing extreme values. Moreover, we focus on the case where the root cause of the extreme values is the same mechanism: a deadline. We exploit known deadlines using dynamic time warp to search for the recurring similar workload peak patterns varying in time and amplitude.

scholarly journals Extreme Value Index Estimation by Means of an Inequality Curve

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1834
Author(s):  
Emanuele Taufer ◽  
Flavio Santi ◽  
Pier Luigi Novi Inverardi ◽  
Giuseppe Espa ◽  
Maria Michela Dickson
Keyword(s):  
Real Data ◽  
Extreme Value ◽  
Extreme Value Index ◽  
Data Sets ◽  
Powerful Method ◽  
Estimation Strategy ◽  
Graphical Interpretation ◽  
Regularly Varying ◽  
Index Estimation

A characterizing property of Zenga (1984) inequality curve is exploited in order to develop an estimator for the extreme value index of a distribution with regularly varying tail. The approach proposed here has a nice graphical interpretation which provides a powerful method for the analysis of the tail of a distribution. The properties of the proposed estimation strategy are analysed theoretically and by means of simulations. The usefulness of the method will be tested also on real data sets.

scholarly journals Learning Manifolds from Non-stationary Streams

2021 ◽  
Author(s):  
Suchismit Mahapatra ◽  
Varun Chandola
Keyword(s):  
Data Distribution ◽  
Gaussian Process Regression ◽  
Real Data ◽  
Streaming Data ◽  
Data Sets ◽  
Dimensional Representation ◽  
Initial Batch ◽  
Reduction Methods ◽  
Theoretical Results

Abstract Streaming adaptations of manifold learning based dimensionality reduction methods, such as Isomap, are based on the assumption that a small initial batch of observations is enough for exact learning of the manifold, while remaining streaming data instances can be cheaply mapped to this manifold. However, there are no theoretical results to show that this core assumption is valid. Moreover, such methods typically assume that the underlying data distribution is stationary and are not equipped to detect, or handle, sudden changes or gradual drifts in the distribution that may occur when the data is streaming. We present theoretical results to show that the quality of a manifold asymptotically converges as the size of data increases. We then show that a Gaussian Process Regression (GPR) model, that uses a manifold-specific kernel function and is trained on an initial batch of sufficient size, can closely approximate the state-of-art streaming Isomap algorithms. The predictive variance obtained from the GPR prediction is then shown to be an effective detector of changes in the underlying data distribution. Results on several synthetic and real data sets show that the resulting algorithm can effectively learn lower dimensional representation of high dimensional data in a streaming setting, while identifying shifts in the generative distribution.

scholarly journals Topics in data analysis using R in extreme value theory

2013 ◽  
Vol 10 (1) ◽  
Author(s):  
Helena Penalva ◽  
Manuela Neves
Keyword(s):  
Applied Sciences ◽  
Data Analysis ◽  
Open Source Software ◽  
Extreme Value Theory ◽  
Extreme Values ◽  
Value Theory ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Data Sets ◽  
Statistics Of Extremes

The statistical Extreme Value Theory has grown gradually from the beginning of the 20th century. Its unquestionable importance in applications was definitely recognized after Gumbel's book in 1958, Statistics of Extremes. Nowadays there is a wide number of applied sciences where extreme value statistics are largely used. So, accurately modeling extreme events has become more and more important and the analysis requires tools that must be simple to use but also should consider complex statistical models in order to produce valid inferences. To deal with accurate, friendly, free and open-source software is of great value for practitioners and researchers. This paper presents a review of the main steps for initializing a data analysis of extreme values in R environment. Some well documented packages are briefly described and two data sets will be considered for illustrating the use of some functions.

scholarly journals New Families of Generalized Lomax Distributions: Properties and Applications

2019 ◽  
Vol 8 (6) ◽  
pp. 51 ◽  
Author(s):  
Ahmad Alzaghal ◽  
Duha Hamed
Keyword(s):  
Maximum Likelihood ◽  
Structural Properties ◽  
Simulation Study ◽  
Real Data ◽  
Extreme Value ◽  
Data Sets ◽  
Extreme Value Distributions ◽  
Method Of Maximum Likelihood ◽  
The Right ◽  
Family Of Distributions

In this paper, we propose new families of generalized Lomax distributions named T-LomaxfYg. Using the methodology of the Transformed-Transformer, known as T-X framework, the T-Lomax families introduced are arising from the quantile functions of exponential, Weibull, log-logistic, logistic, Cauchy and extreme value distributions. Various structural properties of the new families are derived including moments, modes and Shannon entropies. Several new generalized Lomax distributions are studied. The shapes of these T-LomaxfYg distributions are very flexible and can be symmetric, skewed to the right, skewed to the left, or bimodal. The method of maximum likelihood is proposed for estimating the distributions parameters and a simulation study is carried out to assess its performance. Four applications of real data sets are used to demonstrate the flexibility of T-LomaxfYg family of distributions in fitting unimodal and bimodal data sets from di erent disciplines.

scholarly journals Estimation of Extreme Values by the Average Conditional Exceedance Rate Method

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
A. Naess ◽  
O. Gaidai ◽  
O. Karpa
Keyword(s):  
Time Series ◽  
Extreme Values ◽  
Practical Interest ◽  
Extreme Value Distribution ◽  
Real Data ◽  
Extreme Value ◽  
Point Of View ◽  
Statistical Dependence ◽  
Sampled Data ◽  
Threshold Method

This paper details a method for extreme value prediction on the basis of a sampled time series. The method is specifically designed to account for statistical dependence between the sampled data points in a precise manner. In fact, if properly used, the new method will provide statistical estimates of the exact extreme value distribution provided by the data in most cases of practical interest. It avoids the problem of having to decluster the data to ensure independence, which is a requisite component in the application of, for example, the standard peaks-over-threshold method. The proposed method also targets the use of subasymptotic data to improve prediction accuracy. The method will be demonstrated by application to both synthetic and real data. From a practical point of view, it seems to perform better than the POT and block extremes methods, and, with an appropriate modification, it is directly applicable to nonstationary time series.

Causal inference for extremes on river networks

2021 ◽  
Author(s):  
Ngoc Tran ◽  
Johannes Buck ◽  
Claudia Kluppelberg
Keyword(s):  
Causal Inference ◽  
Extreme Values ◽  
Fundamental Problem ◽  
Nonlinear Models ◽  
Real Data ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Open Problems ◽  
Intractable Likelihood ◽  
Effect Relation

<p>Causal inference for extreme aims to discover cause and effect relation between large observed values of random variables. This is a fundamental problem to in many applications, from finance, engineering risks, nutrition to hydrology, to name a few. Unique challenges to<br>extreme values are lack of data and lack of model smoothness due to the max operator. Existing methods in extreme value statistics for dimensions d ≥ 3 are limited due to an intractable likelihood, while techniques for learning Bayesian networks require a large amount of data to fit nonlinear models. This talk showcases the max-linear model and new algorithms for fitting them. Our method performs well on real data, recovering a directed graph for both the Danube and the Lower Colorado with high accuracy purely through extreme measurements. We also compare our method to state-of-the-art algorithms for causal inference for nonlinear models, and outline open problems in hydrology, extreme value statistics and machine learning.</p>

Comparison of robust logistic regression estimators for variables with generalized extreme value distributions

2021 ◽  
Vol 16 (3) ◽  
pp. 177-187
Author(s):  
Şaban Kızılarslan ◽  
Ceren Camkıran
Keyword(s):  
Logistic Regression ◽  
Regression Model ◽  
Logistic Regression Model ◽  
Extreme Values ◽  
Real Data ◽  
Extreme Value ◽  
Small Samples ◽  
Robust Estimators ◽  
Generalized Extreme Value ◽  
Explanatory Variables

The aim of this study is to compare the performance of robust estimators in the presence of explanatory variables with Generalized Extreme Value (GEV) distributions in the logistic regression model. Existence of extreme values in the logistic regression model negatively affects the bias and effectiveness of classical Maximum Likelihood (ML) estimators. For this reason, robust estimators that are less sensitive to extreme values have been developed. Random variables with extreme values may be fit in one of specific distributions. In study, the GEV distribution family was examined and five robust estimators were compared for the Fréchet, Gumbel and Weibull distributions. To the simulation results, the CUBIF estimator is prominent according to both bias and efficiency criteria for small samples. In medium and large samples, while the MALLOWS estimator has the minimum bias, the CUBIF estimator has the best efficiency. The same results apply for different contamination ratios and different scale parameter values of the distributions. Simulation findings were supported by a meteorological real data application.

scholarly journals The Exponentiated Generalized Topp Leone-G Family of Distributions: Properties and Applications

2019 ◽  
Vol 15 (1) ◽  
pp. 1-24 ◽  
Author(s):  
Hesham Mohamed Reyad ◽  
Morad Alizadeh ◽  
Farrukh Jamal ◽  
Soha Othman ◽  
G G Hamedani
Keyword(s):  
Extreme Values ◽  
Residual Life ◽  
Information Matrix ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
New Class ◽  
New Family ◽  
Mathematical Properties

In this paper, we propose a new class of continuous distributions called the exponentiated generalized Topp Leone-G family that extends the Topp Leone-G family introduced by Al-Shomrani et al. (2016). We derive explicit expressions for certain mathematical properties of the new family such as; ordinary and incomplete moments, generating functions, reliability analysis, Lorenz and Bonferroni curves, Rényi entropy, stress strength model, moment of residual and reversed residual life, order statistics and extreme values. We discuss the maximum likelihood estimates and the observed information matrix for the model parameters. Two real data sets are used to illustrate the flexibility of the new family.

Sign in / Sign up

Export Citation Format

Share Document