Statistical Properties and Applications of Correlated Length Intervals of Some Stationary Random Point Processes

Abstract

The point process, a sequence of random univariate random variables derived from correlated bivariate random variables as modeled by Arnold and Strauss, has been examined. Statistical properties of the time intervals between the points as well as the probability distributions of the number of points registered in a finite interval have been analyzed specifically in function of the coefficient of correlation. The results have been applied to binary detection and to the transmission of information. Both the probability of error and the cut-off rate have been bounded. Several simulations have been generated to illustrate the theoretical results.