Abstract
This paper documents the results of investigations on the variance and covariance properties of mean values within the theory of stationary random functions under a variety of conditions. Analytical expressions have been developed in each case, to facilitate direct and ready applications of the results, using the exponential function as a working model for the covariance function. These properties, in turn, have been utilized in developing mathematical expressions for estimation accuracy (error variance) of the mean estimates for one-dimensional sampling plans. Two distinctly different sampling plans have been discussed: “punctual” sampling with no significant linear extensions of the samples and “linear” sampling with significant linear extensions of samples in the direction of the section being sampled.
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Singh, T.R.P. Analytical studies on some statistical properties of mean values and their applications to sampling in one dimension. Mathematical Geology 10, 169–193 (1978). https://doi.org/10.1007/BF01032863
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DOI: https://doi.org/10.1007/BF01032863