Mean range of linearly dependent normal variables with application to storage problems.

The exact equations for the mean range of some normal but autocorrelated variables, of known population means and known linear dependence, are developed. The basic hypothesis was that the exact expression in the general form for the mean range of linearly dependent normal variables is the same as for the normal independent variable, which form was derived from the mean range given by Anis and Lloyd. The data generation method (with a large sample of 250,000 random numbers) was used to assess the differences in mean ranges between the developed equations and the computer results. For three cases-the first-and the second-order Markov linear dependence and the simple moving average scheme-these differences are very small, and they are of the order of magnitude of the sampling errors for the data generation method. The expressions for exact values of mean range are derived for: (1) the general Markov linear dependence model; (2) the first-order Markov linear dependence; (3) the general linear moving average scheme; and (4) the simple linear moving average scheme. [ABSTRACT FROM AUTHOR]