• Journal of Korean Society for Quality Management
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• v.15 no.2
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• pp.27-37
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• 1987

In life testing problem, many authors obtained the minimum variance unbiased estimator of $P_r$[X>Y] for the exponential family generally and conceptually. In this paper, we study the maximum likelihood estimator and minimum variance unbiased estimator of $P_r$[X>Y] in exponential X and normal Y.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.523-559
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• 2001

To predict the fate of groundwater contaminants, accurate spatially continuous information is needed. Because most field sampling of groundwater contaminants are not conducted spatially continuous manner, a special estimation technique is required to interpolate/extrapolate concentration distributions at unmeasured locations. A practical three-dimensional estimations method for in situ groundwater contaminant concentrations is introduced. It consistas of two general steps: estimation of macroscopic transport process and kriging. Using field data and nonlinear optimization techniques, the macroscopic behavior of the contaminant plume is estimated. A spatial distribution of residuals is obtained by subtracting the macroscopic transport portion from field data, then kriging is applied to estimate residuals at unsampled locations. To reduce outlier effects on obtaining correlations between residual data which are needed for determining variougram models, the R(sub)p-estimator is introduced. The proposed estimation method is applied to a field data set.