• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.25-32
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• 2003

In this paper, we define the mean life process for the right censored data and show the asymptotic equivalence between two kinds of the mean life processes. We use the Kaplan-Meier and Susarla-Van Ryzin estimates as the estimates of survival function for the construction of the mean life processes. Also we show the asymptotic equivalence between two mean residual life processes as an application and finally discuss some difficulties caused by the censoring mechanism.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.635-648
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• 2022

In this paper, we establish an asymptotic formula for mean value of $L^{(k)}({\frac{1}{2}},\;{\chi}_P)$ averaging over ℙ_2g+1 and over ℙ_2g+2 as g → ∞ in odd characteristic. We also give an asymptotic formula for mean value of $L^{(k)}({\frac{1}{2}},\;{\chi}_u)$ averaging over 𝓘_g+1 and over 𝓕_g+1 as g → ∞ in even characteristic.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.229-235
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• 2001

Let {X$\_$n/, n$\geq$1] be a stationary sequence of negatively associated random variables with distribution function F(x)=P(X$_1$$\leq$x). The empirical distribution function F$\_$n/(x) based on X$_1$, X$_2$,....., X$\_$n/ is proposed as an estimator for F$\_$n/(x). Strong consistency and asymptotic normality of F$\_$n/(x) are studied. We also apply these ideas to estimation of the survival function.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.47-62
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• 1997

This paper is concerned with investigating the global as-ymptotic behavior of the zero solution of the initial-boundary value problem for a nonlinear fourth order wave equation, Moreover an esti-mate of the rate of decay of the solutions is obtained.

• Proceedings of the Korean Reliability Society Conference
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• 2000.11a
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• pp.363-363
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• 2000

We derive an asymptotic relation between the scores for the censored and uncensored observations for the untied value case among uncensored observations. With this relation, we show that two types of the linear rank statistics which are based on any consistent estimates of the distribution function, are asymptotically equivalent. Also, we discuss another asymptotic equivalence considered by Cuzick (1985).

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.385-393
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• 2003

Let Y(t) be a stochastic integral process represented by Brownian motion. We show that YHt (t) is continuous in t with probability one for Molder function Ht of exponent ${\beta}$ and finally we derive asymptotic self-similar process YM (t) which converges to Yw (t).

• Journal of the Korean Data and Information Science Society
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• v.20 no.6
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• pp.1169-1175
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• 2009

In this paper, the inferences of data obtained from periodic inspection and type I censoring for the step-stress accelerated life test are studied. The exponential distribution with a failure rate function that a log-linear function of stress and the tampered failure rate model are considered. The maximum likelihood estimators of the model parameters are estimated and also the optimal stress change time which minimize the asymptotic variance of maximum likelihood estimators of parameters is determined. A numerical example will be given to illustrate the proposed inferential procedures and the sensitivity of the asymptotic variance of the estimated mean by the guessed parameters is investigated.

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.223-240
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• 2020

The paper is concerned with periodic linear evolution equations of the form x"(t) = A(t)x(t)+f(t), where A(t) is a family of (unbounded) linear operators in a Banach space X, strongly and periodically depending on t, f is an almost (or asymptotic) almost periodic function. We study conditions for this equation to have almost periodic solutions on ℝ as well as to have asymptotic almost periodic solutions on ℝ⁺. We convert the second order equation under consideration into a first order equation to use the spectral theory of functions as well as recent methods of study. We obtain new conditions that are stated in terms of the spectrum of the monodromy operator associated with the first order equation and the frequencies of the forcing term f.

• Journal of the Korean Statistical Society
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• v.36 no.1
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• pp.57-76
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• 2007

Kriging is a nonparametric regression method used in geostatistics for estimating curves and surfaces for spatial data. It may come as a surprise that the Kriging estimator, normally derived as the best linear unbiased estimator, is also the solution of a particular variational problem. Thus, Kriging estimators can also be interpreted as generalized smoothing splines where the roughness penalty is determined by the covariance function of a spatial process. We build off the early work by Silverman (1982, 1984) and the analysis by Cox (1983, 1984), Messer (1991), Messer and Goldstein (1993) and others and develop an equivalent kernel interpretation of geostatistical estimators. Given this connection we show how a given covariance function influences the bias and variance of the Kriging estimate as well as the mean squared prediction error. Some specific asymptotic results are given in one dimension for Matern covariances that have as their limit cubic smoothing splines.

• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.101-116
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• 1997

This is primarily an expository paper that presents several nonparametric procedures for testing exponentiality against certain monotonicity properties of the mean residual life function, tests against the trend change in such function attract a great deal of attention of late in reliability analysis. In this note, we present some of the known testing procedures regarding the behavior of mean residual life function. These tests are also compared in terms of asymptotic relative efficiency and empirical power against a few alternatives. The tests based on incomplete data are also briefly discussed.