• Journal of the Korean Statistical Society
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• v.35 no.4
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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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• v.16 no.5
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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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• v.17 no.3
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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.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2001.10a
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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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• v.18 no.1
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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.

• Survey Research
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• v.7 no.2
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• pp.53-69
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• 2006

Weights can be made and imposed in both sample design stage and analysis stage in a sample survey. While in design stage weights are related with sample data acquisition quantities such as sample selection probability and response rate, in analysis stage weights are connected with external quantities, for instance population quantities and some auxiliary information. The final weight is the product of all weights in both stage. In the present paper, we focus on the weight in analysis stage and investigate the effect of such weights imposed on the weighted mean when estimating the population mean. We consider a finite population with a pair of fixed survey value and weight in each unit, and suppose equal selection probability designs. Under the condition we derive the formulas of the bias as well as mean square error of the weighted mean and show that the weighted mean is biased and the direction and amount of the bias can be explained by the correlation between survey variate and weight: if the correlation coefficient is positive, then the weighted mein over-estimates the population mean, on the other hand, if negative, then under-estimates. Also the magnitude of bias is getting larger when the correlation coefficient is getting greater. In addition to theoretical derivation about the weighted mean, we conduct a simulation study to show quantities of the bias and mean square errors numerically. In the simulation, nine weights having correlation coefficient with survey variate from -0.2 to 0.6 are generated and four sample sizes from 100 to 400 are considered and then biases and mean square errors are calculated in each case. As a result, in the case or 400 sample size and 0.55 correlation coefficient, the amount or squared bias of the weighted mean occupies up to 82% among mean square error, which says the weighted mean might be biased very seriously in some cases.