• 제목, 요약, 키워드: stationary distribution

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기후변화에 따른 하수관거시설의 계획우수량 산정을 위한 일반극치분포 분석 (Analysis of Generalized Extreme Value Distribution to Estimate Storm Sewer Capacity Under Climate Change)

  • 이학표;류재나;유순유;박규홍
    • 상하수도학회지
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    • v.26 no.2
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    • pp.321-329
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    • 2012
  • In this study, statistical analysis under both stationary and non-stationary climate was conducted for rainfall data measured in Seoul. Generalised Extreme Value (GEV) distribution and Gumbel distribution were used for the analysis. Rainfall changes under the non-stationary climate were estimated by applying time variable (t) to location parameter (${\xi}$). Rainfall depths calculated in non-stationary climate increased by 1.1 to 6.2mm and 1.0 to 4.6mm for the GEV distribution and gumbel distribution respectively from those stationary forms. Changes in annual maximum rainfall were estimated with rate of change in the location parameter (${\xi}1{\cdot}t$), and temporal changes of return period were predicted. This was also available for re-evaluating the current sewer design return period. Design criteria of sewer system was newly suggested considering life expectance of the system as well as temporal changes in the return period.

M/PH/1 QUEUE WITH DETERMINISTIC IMPATIENCE TIME

  • Kim, Jerim;Kim, Jeongsim
    • 대한수학회논문집
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    • v.28 no.2
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    • pp.383-396
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    • 2013
  • We consider an M/PH/1 queue with deterministic impatience time. An exact analytical expression for the stationary distribution of the workload is derived. By modifying the workload process and using Markovian structure of the phase-type distribution for service times, we are able to construct a new Markov process. The stationary distribution of the new Markov process allows us to find the stationary distribution of the workload. By using the stationary distribution of the workload, we obtain performance measures such as the loss probability, the waiting time distribution and the queue size distribution.

On Weak Convergence of Some Rescaled Transition Probabilities of a Higher Order Stationary Markov Chain

  • Yun, Seok-Hoon
    • Journal of the Korean Statistical Society
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    • v.25 no.3
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    • pp.313-336
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    • 1996
  • In this paper we consider weak convergence of some rescaled transi-tion probabilities of a real-valued, k-th order (k $\geq$ 1) stationary Markov chain. Under the assumption that the joint distribution of K + 1 consecutive variables belongs to the domain of attraction of a multivariate extreme value distribution, the paper gives a sufficient condition for the weak convergence and characterizes the limiting distribution via the multivariate extreme value distribution.

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Existence Condition for the Stationary Ergodic New Laplace Autoregressive Model of order p-NLAR(p)

  • Kim, Won-Kyung;Lynne Billard
    • Journal of the Korean Statistical Society
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    • v.26 no.4
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    • pp.521-530
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    • 1997
  • The new Laplace autoregressive model of order 2-NLAR92) studied by Dewald and Lewis (1985) is extended to the p-th order model-NLAR(p). A necessary and sufficient condition for the existence of an innovation sequence and a stationary ergodic NLAR(p) model is obtained. It is shown that the distribution of the innovation sequence is given by the probabilistic mixture of independent Laplace distributions and a degenrate distribution.

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Stationary analysis of the surplus process in a risk model with investments

  • Lee, Eui Yong
    • Journal of the Korean Data and Information Science Society
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    • v.25 no.4
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    • pp.915-920
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    • 2014
  • We consider a continuous time surplus process with investments the sizes of which are independent and identically distributed. It is assumed that an investment of the surplus to other business is made, if and only if the surplus reaches a given sufficient level. We establish an integro-differential equation for the distribution function of the surplus and solve the equation to obtain the moment generating function for the stationary distribution of the surplus. As a consequence, we obtain the first and second moments of the level of the surplus in an infinite horizon.

기후변화에 따른 주요 도시의 하수도 침수 재현기간 예측 (Prediction of Return Periods of Sewer Flooding Due to Climate Change in Major Cities)

  • 박규홍;유순유;뱜바도지 엘베자르갈
    • 상하수도학회지
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    • v.30 no.1
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    • pp.41-49
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    • 2016
  • In this study, rainfall characteristics with stationary and non-stationary perspectives were analyzed using generalized extreme value (GEV) distribution and Gumbel distribution models with rainfall data collected in major cities of Korea to reevaluate the return period of sewer flooding in those cities. As a result, the probable rainfall for GEV and Gumbel distribution in non-stationary state both increased with time(t), compared to the stationary probable rainfall. Considering the reliability of ${\xi}_1$, a variable reflecting the increase of storm events due to climate change, the reliability of the rainfall duration for Seoul, Daegu, and Gwangju in the GEV distribution was over 90%, indicating that the probability of rainfall increase was high. As for the Gumbel distribution, Wonju, Daegu, and Gwangju showed the higher reliability while Daejeon showed the lower reliability than the other cities. In addition, application of the maximum annual rainfall change rate (${\xi}_1{\cdot}t$) to the location parameter made possible the prediction of return period by time, therefore leading to the evaluation of design recurrence interval.

Stationary Distribution for the Mobilities in Catastrophe Rescue Scenario

  • Wang, Yong;Peng, Wei;Dou, Qiang;Gong, Zhenghu
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.7 no.2
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    • pp.308-326
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    • 2013
  • Mobility Model has drawn more and more attentions since its critical role in Mobile Wireless Networks performance evaluation. This paper analyzes the mobility patterns in the catastrophe rescue scenario, and proposes the Random Waypoint with Base Point mobility model to model these characteristics. We mathematically analyze the speed and spatial stationary distributions of the nodes and derive explicit expressions for the one dimensional case. In order to keep the stationary distribution through the entire simulation procedure, we provide strategies to initialize the speed, location and destination of the nodes at the beginning of the simulation. The simulation results verify the derivations and the proposed methods in this paper. This work gives a deep understanding of the properties of the Random Waypoint with Base Point mobility model and such understanding is necessary to avoid misinterpretation of the simulation results. The conclusions are of practical value for performance analysis of mobile wireless networks, especially for the catastrophe rescue scenario.

전국 확률강수량 산정을 위한 비정상성 빈도해석 기법의 적용 (Application of a Non-stationary Frequency Analysis Method for Estimating Probable Precipitation in Korea)

  • 김광섭;이기춘
    • 한국농공학회논문집
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    • v.54 no.5
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    • pp.141-153
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    • 2012
  • In this study, we estimated probable precipitation amounts at the target year (2020, 2030, 2040) of 55 weather stations in Korea using the 24 hour annual maximum precipitation data from 1973 through 2009 which should be useful for management of agricultural reservoirs. Not only trend tests but also non-stationary tests were performed and non-stationary frequency analysis were conducted to all of 55 sites. Gumbel distribution was chosen and probability weighted moment method was used to estimate model parameters. The behavior of the mean of extreme precipitation data, scale parameter, and location parameter were analyzed. The probable precipitation amount at the target year was estimated by a non-stationary frequency analysis using the linear regression analysis for the mean of extreme precipitation data, scale parameter, and location parameter. Overall results demonstrated that the probable precipitation amounts using the non-stationary frequency analysis were overestimated. There were large increase of the probable precipitation amounts of middle part of Korea and decrease at several sites in Southern part. The non-stationary frequency analysis using a linear model should be applicable to relatively short projection periods.

STATIONARY SOLUTIONS FOR ITERATED FUNCTION SYSTEMS CONTROLLED BY STATIONARY PROCESSES

  • Lee, O.;Shin, D.W.
    • 대한수학회지
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    • v.36 no.4
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    • pp.737-746
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    • 1999
  • We consider a class of discrete parameter processes on a locally compact Banach space S arising from successive compositions of strictly stationary random maps with state space C(S,S), where C(S,S) is the collection of continuous functions on S into itself. Sufficient conditions for stationary solutions are found. Existence of pth moments and convergence of empirical distributions for trajectories are proved.

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EFFICIENT ESTIMATION OF THE COINTEGRATING VECTOR IN ERROR CORRECTION MODELS WITH STATIONARY COVARIATES

  • Seo, Byeong-Seon
    • Journal of the Korean Statistical Society
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    • v.34 no.4
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    • pp.345-366
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    • 2005
  • This paper considers the cointegrating vector estimator in the error correction model with stationary covariates, which combines the stationary vector autoregressive model and the nonstationary error correction model. The cointegrating vector estimator is shown to follow the locally asymptotically mixed normal distribution. The variance of the estimator depends on the co­variate effect of stationary regressors, and the asymptotic efficiency improves as the magnitude of the covariate effect increases. An economic application of the money demand equation is provided.