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.

Mean-of-order p reduced-bias extreme value index estimation under a third-order framework

Extremes ◽  
2016 ◽  
Vol 19 (4) ◽  
pp. 561-589 ◽  
Author(s):  
Frederico Caeiro ◽  
M. Ivette Gomes ◽  
Jan Beirlant ◽  
Tertius de Wet
Keyword(s):  
Extreme Value ◽  
Extreme Value Index ◽  
Third Order ◽  
Index Estimation

scholarly journals On Extreme Value Index Estimation under Random Censoring

2018 ◽  
Vol 5 (2) ◽  
pp. 419-445
Author(s):  
Richard Minkah ◽  
Tertius de Wet ◽  
Kwabena Doku-Amponsah
Keyword(s):  
Extreme Value ◽  
Extreme Value Index ◽  
Random Censoring ◽  
Index Estimation

scholarly journals Tail product-limit process for truncated data with application to extreme value index estimation

Extremes ◽  
2016 ◽  
Vol 19 (2) ◽  
pp. 219-251 ◽  
Author(s):  
Souad Benchaira ◽  
Djamel Meraghni ◽  
Abdelhakim Necir
Keyword(s):  
Extreme Value ◽  
Extreme Value Index ◽  
Truncated Data ◽  
Limit Process ◽  
Product Limit ◽  
Index Estimation

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.

Lehmer's mean-of-order-p extreme value index estimation: a simulation study and applications

2019 ◽  
Vol 47 (13-15) ◽  
pp. 2825-2845 ◽  
Author(s):  
Helena Penalva ◽  
M. Ivette Gomes ◽  
Frederico Caeiro ◽  
M. Manuela Neves
Keyword(s):  
Simulation Study ◽  
Extreme Value ◽  
Extreme Value Index ◽  
Index Estimation

Regional extreme value index estimation and a test of tail homogeneity

2015 ◽  
Vol 27 (2) ◽  
pp. 103-115 ◽  
Author(s):  
Paul Kinsvater ◽  
Roland Fried ◽  
Jona Lilienthal
Keyword(s):  
Extreme Value ◽  
Extreme Value Index ◽  
Index Estimation

scholarly journals Learning Strictly Orthogonal p-Order Nonnegative Laplacian Embedding via Smoothed Iterative Reweighted Method

2019 ◽  
Author(s):  
Haoxuan Yang ◽  
Kai Liu ◽  
Hua Wang ◽  
Feiping Nie
Keyword(s):  
Optimization Problem ◽  
Empirical Studies ◽  
High Dimensional Data ◽  
Real Data ◽  
High Dimensional ◽  
Data Sets ◽  
Powerful Method ◽  
Intrinsic Geometry ◽  
L2 Norm ◽  
Nonnegative Constraints

Laplacian Embedding (LE) is a powerful method to reveal the intrinsic geometry of high-dimensional data by using graphs. Imposing the orthogonal and nonnegative constraints onto the LE objective has proved to be effective to avoid degenerate and negative solutions, which, though, are challenging to achieve simultaneously because they are nonlinear and nonconvex. In addition, recent studies have shown that using the p-th order of the L2-norm distances in LE can find the best solution for clustering and promote the robustness of the embedding model against outliers, although this makes the optimization objective nonsmooth and difficult to efficiently solve in general. In this work, we study LE that uses the p-th order of the L2-norm distances and satisfies both orthogonal and nonnegative constraints. We introduce a novel smoothed iterative reweighted method to tackle this challenging optimization problem and rigorously analyze its convergence. We demonstrate the effectiveness and potential of our proposed method by extensive empirical studies on both synthetic and real data sets.

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.

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