Statistics of Hyperbolic Error Distributions in Data Transmission

Error bursts in data transmission systems do not usually occur completely at random. It has been found that often they follow a hyperbolic rather than a Poisson distribution. Several statistical quantities consistent with the hyperbolic distribution have been developed. These are compared with the corresponding quantities for a Poisson distribution. Specifically, the quantities are the probability of exactly bursts in a time interval for which the long-time average is , the cumulative probability of at least bursts in this time interval, and the cumulative probability of burstfree stretches of time intervals or longer.