Analysis of the Pareto Model for Error Statistics on Telephone Circuits

A statistical model for the occurrence of errors in data transmission over telephone circuits was recently proposed by Berger and Mandelbrot. In their model the intervals between successive errors are distributed independently according to the Pareto distribution . This paper presents an analysis based on the Pareto model and compares the results with published measurements on telephone networks. Statistics, such as the probability of zero, one or two errors in a block of digits, and the probability of error-free transmission runs for no-error correction or single-error correction codes are derived. Comparison with experiments indicates that the Pareto distribution provides an excellent representation of the error statistics.