• Title/Summary/Keyword: long-tail distribution

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Extreme value modeling of structural load effects with non-identical distribution using clustering

  • Zhou, Junyong;Ruan, Xin;Shi, Xuefei;Pan, Chudong
    • Structural Engineering and Mechanics
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    • v.74 no.1
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    • pp.55-67
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    • 2020
  • The common practice to predict the characteristic structural load effects (LEs) in long reference periods is to employ the extreme value theory (EVT) for building limit distributions. However, most applications ignore that LEs are driven by multiple loading events and thus do not have the identical distribution, a prerequisite for EVT. In this study, we propose the composite extreme value modeling approach using clustering to (a) cluster initial blended samples into finite identical distributed subsamples using the finite mixture model, expectation-maximization algorithm, and the Akaike information criterion; (b) combine limit distributions of subsamples into a composite prediction equation using the generalized Pareto distribution based on a joint threshold. The proposed approach was validated both through numerical examples with known solutions and engineering applications of bridge traffic LEs on a long-span bridge. The results indicate that a joint threshold largely benefits the composite extreme value modeling, many appropriate tail approaching models can be used, and the equation form is simply the sum of the weighted models. In numerical examples, the proposed approach using clustering generated accurate extrema prediction of any reference period compared with the known solutions, whereas the common practice of employing EVT without clustering on the mixture data showed large deviations. Real-world bridge traffic LEs are driven by multi-events and present multipeak distributions, and the proposed approach is more capable of capturing the tendency of tailed LEs than the conventional approach. The proposed approach is expected to have wide applications to general problems such as samples that are driven by multiple events and that do not have the identical distribution.

Estimation on composite lognormal-Pareto distribution based on doubly censored samples (결합 로그노말-파레토 분포에서 추출된 양쪽 중도 절단된 표본을 이용한 모수추정)

  • Lee, Kwang-Ho
    • Journal of the Korean Data and Information Science Society
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    • v.22 no.2
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    • pp.171-177
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    • 2011
  • With the development of the actuarial and insurance industries, the distributions of the insurance payments data are deeply studied by many authors. It is known that theses types of distribution are very highly positively skewed and have a long thick upper tail such as Pareto or lognormal distribution. In 2005, Cooray and Ananda proposed a new model which is composed lognormal distribution and Pareto distribution. They said it as composite lognormal-Preto distribution. They showed that the proposed distribution was better fitted than lognormal or Pareto distribution. On the other hand many agreements about the insurance payment have some options for a trivially small payment or extremely large one because of the limits of total payment. Appling these cases, in this paper we consider the parameter estimation on the composite lognormal-Pareto distribution based on doubly censored samples.

A Study of Power Law Distribution of Korean Disaster and Identification of Focusing Events (한국 재난의 멱함수분포와 사회적 충격사건에 관한 연구)

  • Kim, Yongkyun;Kim, Sang Pil;Cho, Hyoung-Sig;Sohn, Hong-Gyoo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.36 no.1
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    • pp.181-190
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    • 2016
  • Improvements in disaster management has become a global necessity because the magnitude of disasters is intensifying in parallel with the increased disaster damage. The disaster risk in Korea is also increasing due to the emergence of new types of disaster; such as the Middle East respiratory syndrome coronavirus, the increase of complex disasters, and the heightened probability of a catastrophic event due to climate change. This paper aimed to identify the disaster loss-frequency relationship from 1948 to 2014 in Korea by using four types of variables. In addition, this paper found major disasters that resulted in the reformation of disaster response organizations, and inputted the deaths and economic loss attributed to those disasters into the disaster loss-frequency graph. The research result substantiated that the disaster loss-frequency relationship in Korea follows the Power Law and found the coefficients of each Power Function. Additionally, this paper found that most of the reformations of disaster response organizations happened after major disasters that concentrated societies attention and anger due to the high human and economic impact; such events are labelled as "focusing events." These focusing events, with the characteristics of a low probability and high impact, are located in the long tail of the Power Law Distribution. This paper suggests that the effective public policy for disaster response needs to be developed by paying attention to 'low probability and high impact' focusing events that are located in the long tail of the Power Law Distribution.

Efficient Inverter Type Compressor System using the Distribution of the Air Flow Rate (공기 변화량 분포를 이용한 효율적인 인버터타입 압축기 시스템)

  • Shim, JaeRyong;Kim, Yong-Chul;Noh, Young-Bin;Jung, Hoe-kyung
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.19 no.10
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    • pp.2396-2402
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    • 2015
  • Air compressor, as an essential equipment used in the factory and plant operations, accounts for around 30% of the total electricity consumption in U.S.A, thereby being proposed advanced technologies to reduce electricity consumption. When the fluctuation of the compressed airflow rate is small, the system stability is increased followed by the reduction of the electricity consumption which results in the efficient design of the energy system. In the statistical analysis, the normal distribution, log normal distribution, gamma distribution or the like are generally used to identify system characteristics. However a single distribution may not fit well the data with long tail, representing sudden air flow rate especially in extremes. In this paper, authors decouple the compressed airflow rate into two parts to present a mixture of distribution function and suggest a method to reduce the electricity consumption. This reduction stems from the fact that a general pareto distribution estimates more accurate quantile value than a gaussian distribution when an airflow rate exceeds over a large number.

Some models for rainfall focused on the inner correlation structure

  • Kim, Sangdan
    • Proceedings of the Korea Water Resources Association Conference
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    • 2004.05b
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    • pp.1290-1294
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    • 2004
  • In this study, new stochastic point rainfall models which can consider the correlation structure between rainfall intensity and duration are developed. In order to consider the negative and positive correlation simultaneously, the Gumbels type-II bivariate distribution is applied, and for the cluster structure of rainfall events, the Neyman-Scott cluster point process is selected. In the theoretical point of view, it is shown that the models considering the dependent structure between rainfall intensity and duration have slightly heavier tail autocorrelation functions than the corresponding independent mode]s. Results from generating long time rainfall events show that the dependent models better reproduce historical rainfall time series than the corresponding independent models in the sense of autocorrelation structures, zero rainfall probabilities and extreme rainfall events.

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A Technique to Circumvent V-shaped Deconvolution Error for Time-dependent SRAM Margin Analyses

  • Somha, Worawit;Yamauchi, Hiroyuki;Yuyu, Ma
    • IEIE Transactions on Smart Processing and Computing
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    • v.2 no.4
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    • pp.216-225
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    • 2013
  • This paper discusses the issues regarding an abnormal V-shaped error confronting algebraic-based deconvolution process. Deconvolution was applied to an analysis of the effects of the Random Telegraph Noise (RTN) and Random Dopant Fluctuation (RDF) on the overall SRAM margin variations. This paper proposes a technique to suppress the problematic phenomena in the algebraic-based RDF/RTN deconvolution process. The proposed technique can reduce its relative errors by $10^{10}$ to $10^{16}$ fold, which is a sufficient reduction for avoiding the abnormal ringing errors in the RTN deconvolution process. The proposed algebraic-based analyses allowed the following: (1) detection of the truncating point of the TD-MV distributions by the screening test, and (2) predicting the MV-shift-amount by the assisted circuit schemes needed to avoid the out of specs after shipment.

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Molecular Dynamics Simulation for Bilayers of Alkyl Thiol Molecules at Solid-Solid Interfaces

  • 이송희;김한수;박형숙
    • Bulletin of the Korean Chemical Society
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    • v.19 no.10
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    • pp.1047-1054
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    • 1998
  • We present the results of molecular dynamics simulations for three different systems of bilayers of long-chain alkyl thiol [S(CH2)15CH3] molecules on an solid-solid interface using the extended collapsed atom model for the chain-molecule. It is found that there exist two possible transitions: a continuous transition characterized by a change in molecular interaction between sites of different chain molecules with increasing area per molecule and a sudden transition from an ordered lattice-like state to a liquid-like state due to the lack of interactions between sites of chain molecules on different surfaces with increasing distance between two solid surfaces. The third system displays a smooth change in probability distribution characterized by the increment of gauche structure in the near-tail part of the chain with increasing area per molecule. The analyses of energetic results and chain conformation results demonstrate the characteristic change of chain structure of each system.

The Characteristics of the Repair Cost Distribution in Apartment Housing

  • Lee, KangHee;Chae, ChangU
    • KIEAE Journal
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    • v.15 no.6
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    • pp.19-26
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    • 2015
  • Purpose: The repair would require to conserve and improve the building function and performance since built. Each household is responsible for maintaining the public facilities and paying the required cost. Therefore, it needs to get the tool or method to forecast the required cost in the future. Before the repair cost is provided, it needs to catch the repair cost distribution and provide the unit cost for the repair cycle. In this study, it aimed at providing the repair cost unit and analyzing the repair cost distribution in a roof proofing work, elevator work and building painting, which are divided into a fully work and partly change. Results of this study are shown that first, the average repair cost for roof proofing work is provided with $166.59{\times}10^3won/household$ and $1.59{\times}10^3won/m^2$ of a full change, $33.22{\times}10^3won/household$ and $0.33{\times}10^3won/m^2$ for a partly work. In addition, elevator work is $557.45{\times}10^3won/household$ and $5.38{\times}10^3won/m^2$ for a full change, $32.92{\times}10^3won/household$ and $0.56{\times}10^3won/m^2$ for a partly repair. Painting has a $304.48{\times}10^3won/household$ and $2.94{\times}10^3won/m^2$. Second, the distribution pattern of repair unit cost has a weibull-typed distribution which has a long tail to the right.

Non-Gaussian feature of fluctuating wind pressures on rectangular high-rise buildings with different side ratios

  • Jia-hui Yuan;Shui-fu Chen;Yi Liu
    • Wind and Structures
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    • v.37 no.3
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    • pp.211-227
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    • 2023
  • To investigate the non-Gaussian feature of fluctuating wind pressures on rectangular high-rise buildings, wind tunnel tests were conducted on scale models with side ratios ranging from 1/9~9 in an open exposure for various wind directions. The high-order statistical moments, time histories, probability density distributions, and peak factors of pressure fluctuations are analyzed. The mixed normal-Weibull distribution, Gumbel-Weibull distribution, and lognormal-Weibull distribution are adopted to fit the probability density distribution of different non-Gaussian wind pressures. Zones of Gaussian and non-Gaussian are classified for rectangular buildings with various side ratios. The results indicate that on the side wall, the non-Gaussian wind pressures are related to the distance from the leading edge. Apart from the non-Gaussianity in the separated flow regions noted by some literature, wind pressures behind the area where reattachment happens present non-Gaussian nature as well. There is a new probability density distribution type of non-Gaussian wind pressure which has both long positive and negative tail found behind the reattachment regions. The correlation coefficient of wind pressures is proved to reflect the non-Gaussianity and a new method to estimate the mean reattachment length of rectangular high-rise building side wall is proposed by evaluating the correlation coefficient. For rectangular high-rise buildings, the mean reattachment length calculated by the correlation coefficient method along the height changes in a parabolic shape. Distributions of Gaussian and non-Gaussian wind pressures vary with side ratios. It is inappropriate to estimate the extreme loads of wind pressures using a fixed peak factor. The trend of the peak factor with side ratios on different walls is given.

Multidisciplinary Design Optimization(MDO) of a Medium-Sized Solar Powered HALE UAV Considering Energy Balancing (에너지 균형조건을 고려한 중형 태양광 추진 고고도 장기체공 무인기의 다분야 통합 최적설계)

  • Park, Kyung-Hyun;Min, Sang-Gyu;Ahn, Jon;Lee, Dong-Ho
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.40 no.2
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    • pp.129-138
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    • 2012
  • A MDO study of a midium-sized solar powered High Altitude Long Endurance (HALE) UAV has been performed, focused on energy balance. In the MDO process, Vortex Lattice Method(VLM) is employed for the aerodynamic modeling of the vehicle, of which structural weight is estimated with the modeling proposed by Cruz. Tail volume ratios have been set as constants, while the location of tail surfaces is determined from longitudinal static stability criterion. By balancing the available energy from solar cells, battery, and altitude, with the energy-requirement of the vehicle, the possibility of continuous flight over 24-hours has been investigated. The solar radiation level is set as that of summer at the latitude of $36^{\circ}$ north. During the daytime, the aircraft climbs using solar energy, accumulating potential energy, which supplements energy balance during the night. Optimizations have been sought in size of the vehicle, its weight distribution, and flight strategy.