• Title, Summary, Keyword: statistics of extremes

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SPATIAL TRENDS AND SPATIAL EXTREMES IN SOUTH KOREAN OZONE

  • Yun, Seok-Hoon;Richard L. Smith
    • Journal of the Korean Statistical Society
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    • v.32 no.4
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    • pp.313-335
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    • 2003
  • Hourly ozone data are available for 73 stations in South Korea from January, 1988 to August, 1998. We are interested in detecting trends in both the mean levels and the extremes of ozone, and in determining how these trends vary over the country. The latter aspect means that we also have to understand the spatial dependence of ozone. In this connection, therefore, we examine in this paper the following features: determining trends in mean ozone levels at individual stations and combination across stations; determining trends in extreme ozone levels at individual stations and combination across stations; spatial modeling of trends in mean and extreme ozone levels.

CONVERGENCE RATES FOR THE MOMENTS OF EXTREMES

  • Peng, Zuoxiang;Nadarajah, Saralees
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.3
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    • pp.495-510
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    • 2012
  • Let $X_1$, $X_2$,${\ldots}$, $X_n$ be a sequence of independent and identically distributed random variables with common distribution function $F$. Convergence rates for the moments of extremes are studied by virtue of second order regularly conditions. A unified treatment is also considered under second order von Mises conditions. Some examples are given to illustrate the results.

Probability of exceeding the serviceability limit of antenna masts

  • Kammel, Christian
    • Wind and Structures
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    • v.4 no.4
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    • pp.353-366
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    • 2001
  • With respect to serviceability, antenna masts should be designed so that wind-induced motion will not cause unacceptable lack of transmission for broadcasting users and wireless communication. For such antenna masts with directional radio transmission the serviceability limit state is predominantly governed by the tolerable change of the broadcasting angle of the mounted antenna assembly and therefore by the tip distortion of the mast. In this paper it will be shown that refinements of the present state of design of antenna masts are possible by using the statistics of extremes applied to extreme wind situations and by consideration of the statistical and reliability requirements given by the operator such as frequency and return period of passing the serviceability limit.

On Numerical Computation of Pickands Constants

  • Choi, Hyemi
    • Communications for Statistical Applications and Methods
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    • v.22 no.3
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    • pp.277-283
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    • 2015
  • Pickands constant $H_{\alpha}$ appears in the classical result about tail probabilities of the extremes of Gaussian processes and there exist several different representations of Pickands constant. However, the exact value of $H_{\alpha}$ is unknown except for two special Gaussian processes. Significant effort has been made to find numerical approximations of $H_{\alpha}$. In this paper, we attempt to compute numerically $H_{\alpha}$ based on its representation derived by $H{\ddot{u}}sler$ (1999) and Albin and Choi (2010). Our estimates are compared with the often quoted conjecture $H_{\alpha}=1/{\Gamma}(1/{\alpha})$ for 0 < ${\alpha}$ ${\leq}$ 2. This conjecture does not seem compatible with our simulation result for 1 < ${\alpha}$ < 2, which is also recently observed by Dieker and Yakir (2014) who devised a reliable algorithm to estimate these constants along with a detailed error analysis.

Threshold Modelling of Spatial Extremes - Summer Rainfall of Korea (공간 극단값의 분계점 모형 사례 연구 - 한국 여름철 강수량)

  • Hwang, Seungyong;Choi, Hyemi
    • The Korean Journal of Applied Statistics
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    • v.27 no.4
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    • pp.655-665
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    • 2014
  • An adequate understanding and response to natural hazards such as heat wave, heavy rainfall and severe drought is required. We apply extreme value theory to analyze these abnormal weather phenomena. It is common for extremes in climatic data to be nonstationary in space and time. In this paper, we analyze summer rainfall data in South Korea using exceedance values over thresholds estimated by quantile regression with location information and time as covariates. We group weather stations in South Korea into 5 clusters and t extreme value models to threshold exceedances for each cluster under the assumption of independence in space and time as well as estimates of uncertainty for spatial dependence as proposed in Northrop and Jonathan (2011).

ON ASYMPTOTIC OF EXTREMES FROM GENERALIZED MAXWELL DISTRIBUTION

  • Huang, Jianwen;Wang, Jianjun
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.3
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    • pp.679-698
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    • 2018
  • In this paper, with optimal normalized constants, the asymptotic expansions of the distribution and density of the normalized maxima from generalized Maxwell distribution are derived. For the distributional expansion, it shows that the convergence rate of the normalized maxima to the Gumbel extreme value distribution is proportional to 1/ log n. For the density expansion, on the one hand, the main result is applied to establish the convergence rate of the density of extreme to its limit. On the other hand, the main result is applied to obtain the asymptotic expansion of the moment of maximum.

CONVERGENCE RATE OF EXTREMES FOR THE GENERALIZED SHORT-TAILED SYMMETRIC DISTRIBUTION

  • Lin, Fuming;Peng, Zuoxiang;Yu, Kaizhi
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.5
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    • pp.1549-1566
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    • 2016
  • Denote $M_n$ the maximum of n independent and identically distributed variables from the generalized short-tailed symmetric distribution. This paper shows the pointwise convergence rate of the distribution of $M_n$ to exp($\exp(-e^{-x})$) and the supremum-metric-based convergence rate as well.

Future Trend in Seasonal Lengths and Extreme Temperature Distributions Over South Korea

  • Lee, Jangho
    • Asia-Pacific Journal of Atmospheric Sciences
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    • v.53 no.1
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    • pp.31-41
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    • 2017
  • CSEOF analysis is conducted on the daily mean, maximum, and minimum temperatures measured at 60 Korea Meteorological Administration stations in the period of 1979-2014. Each PC time series is detrended and fitted to an autoregressive (AR) model. The resulting AR models are used to generate 100 sets of synthetic PC time series for the period of 1979-2064, and the linear trends are added back to the resulting PC time series. Then, 100 sets of synthetic daily temperatures are produced by using the synthetic PC time series together with the The cyclostationary EOF (CSEOF) loading vectors. The statistics of the synthetic daily temperatures are similar to those of the original data during the observational period (1979-2064). Based on the synthetic datasets, future statistics including distribution of extreme temperatures and the length of four seasons have been analyzed. Average daily temperature in spring is expected to decrease by a small amount, whereas average temperatures in summer, fall and winter are expected to increase. Standard deviation of daily temperatures is expected to increase in all four seasons. The Generalized Extreme Value and Generalized Pareto distributions of extreme temperatures indicate that both warm and cold extremes are likely to increase in summer, while only warm extremes are predicted to increase significantly in winter. Thus, heat waves will increase and cold waves will decrease in number in future. Spring and fall will be shorter, whereas summer and winter will be longer. A statistical prediction carried out in the present study may serve as a baseline solution for numerical predictions using complex models.

A class of CUSUM tests using empirical distributions for tail changes in weakly dependent processes

  • Kim, JunHyeong;Hwang, Eunju
    • Communications for Statistical Applications and Methods
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    • v.27 no.2
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    • pp.163-175
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    • 2020
  • We consider a wide class of general weakly-dependent processes, called ψ-weak dependence, which unify almost all weak dependence structures of interest found in statistics under natural conditions on process parameters, such as mixing, association, Bernoulli shifts, and Markovian sequences. For detecting the tail behavior of the weakly dependent processes, change point tests are developed by means of cumulative sum (CUSUM) statistics with the empirical distribution functions of sample extremes. The null limiting distribution is established as a Brownian bridge. Its proof is based on the ψ-weak dependence structure and the existence of the phantom distribution function of stationary weakly-dependent processes. A Monte-Carlo study is conducted to see the performance of sizes and powers of the CUSUM tests in GARCH(1, 1) models; in addition, real data applications are given with log-returns of financial data such as the Korean stock price index.

Evaluation of the major sources of atmospheric pollution in jilin city by regression diagnostics (대기 오염이 암에 의한 사망률에 미치는 영향에 관한 연구)

  • 한지농;우치수
    • The Korean Journal of Applied Statistics
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    • v.2 no.2
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    • pp.47-51
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    • 1989
  • We study by stepwise regression method, the influence which atmospheric pollution in Jilin City has on the rate of death accorrding to cancer. The extremes are discovered and we know that $SO_2$ and smoking are important factors too.

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