scholarly journals On the tails of distributions of annual peak flow

2011 ◽  
Vol 42 (2-3) ◽  
pp. 171-192 ◽  
Author(s):  
Witold G. Strupczewski ◽  
Krzysztof Kochanek ◽  
Iwona Markiewicz ◽  
Ewa Bogdanowicz ◽  
Stanislaw Weglarczyk ◽  
...  
Keyword(s):  
Flood Frequency ◽  
Correct Selection ◽  
Data Sets ◽  
Frequency Model ◽  
Peak Flows ◽  
Annual Peak ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Log Normal ◽  
Selection Of

This study discusses an application of heavy-tailed distributions to modelling of annual peak flows in general and of Polish data sets in particular. One- and two-shape parameter heavy-tailed distributions are obtained by transformations of random variables. The correct selection of a flood frequency model with emphasis on heavy-tailed distribution discrimination is then discussed. If a distribution is wrongly assumed, the error, in the upper quantile, arising as a result, depends on the method of parameter estimation and is shown analytically for three methods. Asymptotic and sampling values (got by simulation) were assessed for the pair log-Gumbel (LG) as a false distribution and log-normal (LN) as a true distribution. Comparing the upper quantiles of various distributions with the same values of moments, it is found that heavy-tailed distributions do not consistently provide higher flood frequency estimates than do soft-tailed distributions. Based on L-moment ratio diagrams and the test of linearity on log–log plots, it is concluded that Polish datasets of annual peak flows should be modelled using soft-tailed distributions, such as the three-parameter Inverse Gaussian, rather than heavy-tailed distributions.

Heavy-tailed distributions for building stock data

2018 ◽  
Vol 46 (7) ◽  
pp. 1281-1296 ◽  
Author(s):  
Patrick Erik Bradley ◽  
Martin Behnisch
Keyword(s):  
Power Law ◽  
Building Stock ◽  
Underlying Distribution ◽  
Large Cities ◽  
Statistical Framework ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed Distribution ◽  
Event Histories ◽  
Heavy Tailed ◽  
Log Normal

The question of inferring the owner of a set of building stocks (e.g. from which country the buildings are taken) from building-related quantities like number of buildings or types of building event histories necessitates the knowledge of their distributions in order to compare them. If the distribution function is a power law, then a version of the 80/20 rule can be applied to describe the variable. This distribution is an example of a heavy-tailed distribution; another example is the log-normal distribution. Heavy-tailed distributions have the property that studying the effects of the few large values already yields most of the overall effect of the whole quantity. For example, if reducing the CO2 emissions of the buildings of a country is the issue, then in case of a heavy-tailed distribution, only the effects of the relatively few large cities need to be considered. It is shown that the number of buildings in German municipalities or counties or the number of building-related event histories of a certain vanished building stock follow a heavy-tailed distribution and give evidence for the type of underlying distribution. The methodology used is a recent statistical framework for discerning power law and other heavy-tailed distributions in empirical data.

Penggunaan Taburan Pareto Umum dalam Menganalisis Nilai Ekstrim Banjir Menggunakan Siri Aliran Puncak Melebihi Paras

2012 ◽  
Author(s):  
Ani Shabri
Keyword(s):  
Poisson Process ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Annual Maximum ◽  
Peaks Over Threshold ◽  
Heavy Tailed Distributions ◽  
Probability Weighted Moment ◽  
Heavy Tailed

Siri banjir tahunan maksimum (Annual Maximum, AM) merupakan pendekatan yang begitu terkenal dalam analisis frekuensi banjir. Siri puncak melebihi paras (peaks over threshold, POT) telah digunakan sebagai alternatif kepada siri banjir tahunan maksimum. Masalah utama dalam pendekatan POT adalah berkaitan pemilihan paras yang sesuai. Dalam kajian ini, kesan perubahaan paras bagi siri POT ke atas nilai anggaran dikaji. Model POT dengan andaian bahawa bilangan puncak melebihi paras bertabur secara Poisson dan magnitud puncak melebihi paras tertabur secara Pareto Umum (General Pareto Distribution, GPD) dibincangkan. Parameter taburan GPD dianggar menggunakan kaedah kebarangkalian pemberat momen (Probability Weighted Moment, PWM) untuk paras yang diketahui. Perbandingan kesesuaian model POT dan model AM dalam menganggarkan nilai hujung atas taburan dibuat. Hasil kajian menunjukkan bahawa apabila paras siri POT boleh disuaikan oleh taburan Pareto dengan proses Poisson, model POT didapati dapat menghasilkan anggaran nilai hujung atas taburan lebih baik berbanding model aliran maksimum. Kata kunci: Siri puncak melebihi paras, proses poisson, taburan pareto umum, GEV, hujung atas taburan Annual maximum flood series remains the most popular approach to flood frequency analysis. Peaks over threshold series have been used as an alternative to annual maximum series. One specific difficulty of the POT approach is the selection of the threshold level. In this study the effect of raising the threshold of the POT series on heavy-tailed distributions estimation is investigated. The POT model described by the generalized Pareto distribution for peak magnitudes with the Poisson process for the occurrence of peaks is discussed. Estimation of the GPD parameters by the method of probability weighted moment (PWM) is formulated for known thresholds. A comparison of the efficiencies of the POT and AM models in heavy-tailed distributions is made. The result showed that when the threshold of POT series can be fitted by GPD with the Poisson process, the POT model is more efficient than the annual maximum (AM) model in estimating the highest extreme value. Key words: Peaks over threshold, poisson process, pareto distribution, GEV, heavy tailed distributions

scholarly journals A New Extended-X Family of Distributions: Properties and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Mi Zichuan ◽  
Saddam Hussain ◽  
Anum Iftikhar ◽  
Muhammad Ilyas ◽  
Zubair Ahmad ◽  
...  
Keyword(s):  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Statistical Distributions ◽  
Reliability Engineering ◽  
Monte Carlo Simulation Study ◽  
Diverse Range ◽  
Heavy Tailed ◽  
Log Normal ◽  
Extended Weibull Distribution

During the past couple of years, statistical distributions have been widely used in applied areas such as reliability engineering, medical, and financial sciences. In this context, we come across a diverse range of statistical distributions for modeling heavy tailed data sets. Well-known distributions are log-normal, log-t, various versions of Pareto, log-logistic, Weibull, gamma, exponential, Rayleigh and its variants, and generalized beta of the second kind distributions, among others. In this paper, we try to supplement the distribution theory literature by incorporating a new model, called a new extended Weibull distribution. The proposed distribution is very flexible and exhibits desirable properties. Maximum likelihood estimators of the model parameters are obtained, and a Monte Carlo simulation study is conducted to assess the behavior of these estimators. Finally, we provide a comparative study of the newly proposed and some other existing methods via analyzing three real data sets from different disciplines such as reliability engineering, medical, and financial sciences. It has been observed that the proposed method outclasses well-known distributions on the basis of model selection criteria.

A THEORETICAL ANALYSIS OF MULTISCALE ENTROPY UNDER THE INVERSE GAUSSIAN DISTRIBUTION

2009 ◽  
Vol 19 (09) ◽  
pp. 3161-3168 ◽  
Author(s):  
YING TANG ◽  
WENJIANG PEI ◽  
KAI WANG ◽  
ZHENYA HE ◽  
YIUMING CHEUNG
Keyword(s):  
Gaussian Distribution ◽  
Theoretical Basis ◽  
Multiple Scales ◽  
Inverse Gaussian Distribution ◽  
Multiscale Entropy ◽  
Data Sets ◽  
Inverse Gaussian ◽  
Heavy Tailed Distributions ◽  
Potential Applications ◽  
Heavy Tailed

Multiscale entropy (MSE) discloses the intrinsic multiple scales in the complexity of physical and physiological signals, which are usually featured by heavy-tailed distributions. Most of these research results are pure experimental search, till Costa et al. made the first attempt to the theoretical basis of MSE. However, the analysis only supports the Gaussian distribution [Phys. Rev. E71, 021906 (2005)]. In this paper, we present the theoretical basis of MSE under the inverse Gaussian distribution, which is a typical model for physiological, physical and financial data sets. The analysis is applicable to uncorrelated inverse Gaussian process and 1/f noise with the multivariate inverse Gaussian distribution, providing a reliable foundation for potential applications of MSE to explore complex physical and physiological time series.

scholarly journals Two symmetric and computationally efficient Gini correlations

2020 ◽  
Vol 8 (1) ◽  
pp. 373-395
Author(s):  
Courtney Vanderford ◽  
Yongli Sang ◽  
Xin Dang
Keyword(s):  
Influence Function ◽  
Random Variables ◽  
Real Data ◽  
Computationally Efficient ◽  
Gini Correlation ◽  
Heavy Tailed Distributions ◽  
Data Application ◽  
Heavy Tailed ◽  
Log Normal ◽  
Log Normal Distribution

AbstractStandard Gini correlation plays an important role in measuring the dependence between random variables with heavy-tailed distributions. It is based on the covariance between one variable and the rank of the other. Hence for each pair of random variables, there are two Gini correlations and they are not equal in general, which brings a substantial difficulty in interpretation. Recently, Sang et al (2016) proposed a symmetric Gini correlation based on the joint spatial rank function with a computation cost of O(n2) where n is the sample size. In this paper, we study two symmetric and computationally efficient Gini correlations with the computational complexity of O(n log n). The properties of the new symmetric Gini correlations are explored. The influence function approach is utilized to study the robustness and the asymptotic behavior of these correlations. The asymptotic relative efficiencies are considered to compare several popular correlations under symmetric distributions with different tail-heaviness as well as an asymmetric log-normal distribution. Simulation and real data application are conducted to demonstrate the desirable performance of the two new symmetric Gini correlations.

scholarly journals Inundation risk for embanked rivers

2013 ◽  
Vol 10 (3) ◽  
pp. 2987-3025 ◽  
Author(s):  
W. G. Strupczewski ◽  
K. Kochanek ◽  
E. Bogdanowicz ◽  
I. Markiewicz
Keyword(s):  
Prolonged Exposure ◽  
High Water ◽  
Flood Frequency ◽  
Parameters Estimation ◽  
Component Model ◽  
Flood Frequency Analysis ◽  
Frequency Model ◽  
Peak Flows ◽  
Flood Peak ◽  
Two Component

Abstract. The Flood Frequency Analysis (FFA) concentrates on probability distribution of peak flows of flood hydrographs. However, examination of floods that haunted and devastated the large parts of Poland lead us to revision of the views on the assessment of flood risk of Polish rivers. It turned out that flooding is caused not only by overflow of the levees' crest but mostly due to the prolonged exposure to high water on levees structure causing dangerous leaks and breaches that threaten their total destruction. This is because, the levees are weakened by long-lasting water pressure and as a matter of fact their damage usually occurs after the culmination has passed the affected location. The probability of inundation is the total of probabilities of exceeding embankment crest by flood peak and the probability of washout of levees. Therefore, in addition to the maximum flow one should consider also the duration of high waters in a river channel. In the paper the new two-component model of flood dynamics: "Duration of high waters–Discharge Threshold–Probability of non-exceedance" (DqF), with the methodology of its parameters estimation was proposed as a completion to the classical FFA methods. Such model can estimate the duration of stages (flows) of an assumed magnitude with a given probability of exceedance. The model combined with the technical evaluation of probability of levees breach due to the d-days duration of flow above alarm stage gives the annual probability of inundation caused by the embankment breaking. The results of theoretical investigation were illustrated by a practical example of the model implementation to the series of daily flow of the Vistula River at Szczucin. Regardless promising results, the method of risk assessment due to prolonged exposure of levees to high water is still in its infancy despite its great cognitive potential and practical importance. Therefore, we would like to point out the need for and usefulness of the DqF model as complementary to the analysis of the flood peak flows, as in classical FFA. The presented two-component model combined with the routine flood frequency model constitutes a new direction in FFA for embanked rivers.

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