• Journal of Wetlands Research
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• v.13 no.3
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• pp.499-514
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• 2011

An underlying assumption of traditional hydrologic frequency analysis is that climate, and hence the frequency of hydrologic events, is stationary, or unchanging over time. Under stationary conditions, the distribution of the variable of interest is invariant to temporal translation. Water resources infrastructure planning and design, such as dams, levees, canals, bridges, and culverts, relies on an understanding of past conditions and projection of future conditions. But, Water managers have always known our world is inherently non-stationary, and they routinely deal with this in management and planning. The aim of this paper is to give a brief introduction to non-stationary extreme value analysis methods. In this paper, a non-stationary hydrologic frequency analysis approach is introduced in order to determine probability rainfall consider changing climate. The non-stationary statistical approach is based on the conditional Generalized Extreme Value(GEV) distribution and Maximum Likelihood parameter estimation. This method are applied to the annual maximum 24 hours-rainfall. The results show that the non-stationary GEV approach is suitable for determining probability rainfall for changing climate, sucha sa trend, Moreover, Non-stationary frequency analyzed using SOI(Southern Oscillation Index) of ENSO(El Nino Southern Oscillation).

• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.649-663
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• 2002

We consider an unlimited fluid queueing model which has Fractional Brownian motion(FBM) as an input and a single server of constant service rate. By using the result of Duffield and O'Connell(6), we investigate the asymptotic tail-distribution of the stationary work-load. When there are multiple homogeneous FBM inputs, the workload distribution is similar to that of the queue with one FBM input; whereas for the heterogeneous sources the asymptotic work-load distributions is dominated by the source with the largest Hurst parameter.

• Korean Management Science Review
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• v.10 no.2
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• pp.27-42
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• 1993

Markov chain models can be used to predict the state of the system in the future. We extend the existing Markov chain models in two ways. For the stationary model, we propose a procedure that obtains the transition probabilities by appling the empirical Bayes method, in which the parameters of the prior distribution in the Bayes estimator are obtained on the collaternal micro data. For non-stationary model, we suggest a procedure that obtains a time-varying transition probabilities as a function of the exogenous variables. To illustrate the effectiveness of our extended models, the models are applied to the macro and micro time-series data generated from actual survey. Our stationary model yields reliable parameter values of the prior distribution. And our non-stationary model can predict the variable transition probabilities effectively.

• Journal of Korean Society of Water and Wastewater
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• v.30 no.1
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• pp.51-58
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• 2016

On account of the increase in water demand and climate change, droughts are in great concern for water resources planning and management. In this study, rainfall characteristics with stationary and non-stationary perspectives were analyzed using Weibull distribution model with 40-year records of annual minimum rainfall depth collected in major cities of Korea. As a result, the non-stationary minimum probable rainfall was expected to decrease, compared with the stationary probable rainfall. The reliability of ${\xi}_1$, a variable reflecting the decrease of the minimum rainfall depth due to climate change, in Wonju, Daegu, and Busan was over 90%, indicating the probability that the minimal rainfall depths in those city decrease is high.

• Journal of the Korean Statistical Society
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• v.25 no.1
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• pp.111-122
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• 1996

A model for a system whose state changes continuously with time is introduced. It is assumed that the system is modeled by a Brownian motion with negative drift and an absorbing barrier at the origin. A repairman arrives according to a Poisson process and repairs the system according to an (s,S) policy, i.e., he increases the state of the system up to S if and only if the state is below s. A partial differential equation is derived for the distribution function of X(t), the state of the system at time t, and the Laplace-Stieltjes transform of the distribution function is obtained by solving the partial differential equation. For the stationary case the explicit expression is deduced for the distribution function of the stationary state of the system.

• 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.

• Journal of the Korean Statistical Society
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• v.28 no.2
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• pp.235-251
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• 1999

In this paper we examine extremal behavior of a $textsc{k}$th-order stationary Markov chain {X\ulcorner} by considering excesses over a high level which typically appear in clusters. Excesses over a high level within a cluster define a cluster damage, i.e., a normalized sum of all excesses within a cluster, and all excesses define a damage point process. Under some distributional assumptions for {X\ulcorner}, we prove convergence in distribution of the cluster damage and obtain a representation for the limiting cluster damage distribution which is well suited for simulation. We also derive formulas for the mean and the variance of the limiting cluster damage distribution. These results guarantee a compound Poisson limit for the damage point process, provided that it is strongly mixing.

• Communications for Statistical Applications and Methods
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• v.20 no.6
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• pp.475-480
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• 2013

The surplus process in a risk model is stochastically analyzed. We obtain the characteristic function of the level of the surplus at a finite time, by establishing and solving an integro-differential equation for the distribution function of the surplus. The characteristic function of the stationary distribution of the surplus is also obtained by assuming that an investment of the surplus is made to other business when the surplus reaches a sufficient level. As a consequence, we obtain the first and second moments of the surplus both at a finite time and in an infinite horizon (in the long-run).

• Journal of Information Processing Systems
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• v.8 no.2
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• pp.191-212
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• 2012

Since a social network by definition is so diverse, the problem of estimating the preferences of its users is becoming increasingly essential for personalized applications, which range from service recommender systems to the targeted advertising of services. However, unlike traditional estimation problems where the underlying target distribution is stationary; estimating a user's interests typically involves non-stationary distributions. The consequent time varying nature of the distribution to be tracked imposes stringent constraints on the "unlearning" capabilities of the estimator used. Therefore, resorting to strong estimators that converge with a probability of 1 is inefficient since they rely on the assumption that the distribution of the user's preferences is stationary. In this vein, we propose to use a family of stochastic-learning based Weak estimators for learning and tracking a user's time varying interests. Experimental results demonstrate that our proposed paradigm outperforms some of the traditional legacy approaches that represent the state-of-the-art technology.

• Communications for Statistical Applications and Methods
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• v.22 no.5
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• pp.463-473
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• 2015

We consider a nonparametric AR(1) model with nonparametric ARCH(1) errors. In order to estimate the unknown function of the ARCH part, we apply the stationary bootstrap procedure, which is characterized by geometrically distributed random length of bootstrap blocks and has the advantage of capturing the dependence structure of the original data. The proposed method is composed of four steps: the first step estimates the AR part by a typical kernel smoothing to calculate AR residuals, the second step estimates the ARCH part via the Nadaraya-Watson kernel from the AR residuals to compute ARCH residuals, the third step applies the stationary bootstrap procedure to the ARCH residuals, and the fourth step defines the stationary bootstrapped Nadaraya-Watson estimator for the ARCH function with the stationary bootstrapped residuals. We prove the asymptotic validity of the stationary bootstrap estimator for the unknown ARCH function by showing the same limiting distribution as the Nadaraya-Watson estimator in the second step.