• Journal of the Korean Statistical Society
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• 제35권4호
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• pp.377-395
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• 2006

In this paper we have suggested a family of chain estimators of the population mean $\bar{Y}$ of a study variate y using two auxiliary variates in two phase (double) sampling assuming that the coefficient of variation of the second auxiliary variable is known. It is well known that chain estimators are traditionally formulated when the population mean $\bar{X}_1$ of one of the two auxiliary variables, say $x_1$, is not known but the population mean $\bar{X}_2$ of the other auxiliary variate $x_2$ is available and $x_1$ has higher degree of positive correlation with the study variate y than $x_2$ has with y, $x_2$ being closely related to $x_1$. Here the classes are constructed when the population mean $\bar{X}_1\;of\;X_1$ is not known and the coefficient of variation $C_{x2}\;of\;X_2$ is known instead of population mean $\bar{X}_2$. Asymptotic expressions for the bias and mean square error (MSE) of the suggested family have been obtained. An asymptotic optimum estimator (AOE) is also identified with its MSE formula. The optimum sample sizes of the preliminary and final samples have been derived under a linear cost function. An empirical study has been carried out to show the superiority of the constructed estimator over others.

• Communications for Statistical Applications and Methods
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• 제16권5호
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• pp.821-840
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• 2009

This article addresses the problem of estimating a family of general population parameter ${\theta}_{({\alpha},{\beta})}$ using auxiliary information in the presence of measurement errors. The general results are then applied to estimate the coefficient of variation $C_Y$ of the study variable Y using the knowledge of the error variance ${\sigma}^2{_U}$ associated with the study variable Y, Based on large sample approximation, the optimal conditions are obtained and the situations are identified under which the proposed class of estimators would be better than conventional estimator. Application of the main result to bivariate normal population is illustrated.

• Communications for Statistical Applications and Methods
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• 제17권3호
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• pp.391-411
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• 2010

For estimating the mean of a finite population, three classes of estimators using multi-auxiliary information with unknown means using two phase sampling in presence of non-response have been proposed with their properties. Asymptotically optimum estimator(AOE) in each class has been identified along with their mean squared error formulae. An empirical study is also given.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2001년도 추계학술대회 논문집
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• pp.199-202
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• 2001

This article deals with stochastic reliability systems that include a repair facility and unreliable machines: the main facility of working and an auxiliary facility of "super-reserve" machines. The number of super-reserve machines are random number with a arbitrarily distribution and working machines break down exponentially. Defective machines line up for repair, whose durations are arbitrarily distributed. Refurbished machines return to the main facility. If the main facility is restored to its original quantity, the repair facility leaves on routine maintenance until all of super-reserve machines are exhausted. Then, the busy period is regenerated. The whole system also falls into the category of closed queues, with more options than those of basic models. The techniques include two-variate Markov and semi-regenerative processes, and a duality principle, to find the probability distribution of the number of intact machines. Explicit formulas obtained demonstrate a relatively effortless use of functionals of the main stochastic characteristics (such as expenses due to repair, maintenance, waiting, and rewards for higher reliability) and optimization of their objective function. Applications include computer networking, human resources, and manufacturing processes.

• Communications for Statistical Applications and Methods
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• 제18권1호
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• pp.111-118
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• 2011

This paper suggests a ratio-cum product estimator of a finite population mean using information on the coefficient of variation and the fcoefficient of kurtosis of auxiliary variate in stratified random sampling. Bias and MSE expressions of the suggested estimator are derived up to the first degree of approximation. The suggested estimator has been compared with the combined ratio estimator and several other estimators considered by Kadilar and Cingi (2003). In addition, an empirical study is also provided in support of theoretical findings.

• 한국조사연구학회지:조사연구
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• 제7권2호
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• pp.53-69
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• 2006

표본조사에서 가중치는 설계 단계와 분석 단계에서 만들어지고 부여될 수 있다. 설계 단계의 가중치는 추출확률이나 응답률 등과 같은 표본 데이터 획득 지표에 관련되어 있고 분석 단계의 가중치는 모집단 수치나 다른 보조 변수정보 등과 같은 외적인 정보와 관련되어 있다. 그리고 최종가중치는 설계 단계의 가중치와 분석 단계의 가중치의 곱으로 만들어진다. 이 논문에서는 분석 단계에서 부여되는 가중치에 초점을 맞추어 가중평균으로 모평균을 추정할 때 가중평균에 포함된 가중치가 모평균 추론에 미치는 영향을 고찰하였다. 유한모집단에서 각 조사단위에 조사변수와 가중치가 쌍으로 있고 표본추출확률이 균등한 경우를 가정하였다. 이러한 조건에서 가중평균의 편향과 평균제곱오차를 구하여 가중평균은 모평균의 편향 추정량임을 보였고, 편향의 방향과 크기는 조사변수와 가중치의 상관관계로 설명할 수 있음을 보였다. 즉, 만일 가중치와 조사변수가 양의 상관관계가 있으면 가중평균은 모평균을 과대 추정하게 되고, 만일 음의 상관관계가 있으면 모평균을 과소 추정하게 된다. 그리고 두 변수의 상관계수가 크면 편향은 증가한다. 가중평균에 대한 이론적인 수식 유도와 함께 편향의 크기와 평균제곱오차의 크기를 수치적으로 검토하기 위하여 모의실험을 실시하였다. 모의실험에서는 상관계수가 -0.2과 0.6사이에 있는 9개의 가중치를 생성하였고, 표본수는 100부터 400까지 고려하여 편향의 크기와 평균제곱오차의 크기를 수치적으로 구하였다. 하나의 결과로써 상관계수가 0.55이고 표본수가 400인 경우에 가중평균의 편향의 제곱이 평균제곱오차에서 차지하는 비율은 무려 82%에 이르는 것으로 나타났는데, 이는 가중평균의 편향이 어떤 경우에는 매우 심각할 수도 있음을 보여주는 것이다.