Analytical studies on some statistical properties of mean values and their applications to sampling in one dimension

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.