Title :
Performance analysis of sequential tests between Poisson processes
Author :
DeLucia, James ; Poor, H. Vincent
Author_Institution :
IDA Center for Commun. Res., Princeton, NJ, USA
fDate :
1/1/1997 12:00:00 AM
Abstract :
The problem of performance computation for sequential tests between Poisson processes is considered. The average sample numbers and error probabilities of the sequential probability ratio test (SPRT) between two homogeneous Poisson processes are known to solve certain delay-differential equations (DDEs). Exact, numerically stable solutions to these DDEs are developed here, and their asymptotic properties are explored. These solutions are seen to be superior to earlier solutions of Dvoretsky, Kiefer, and Wolfowitz (1953), which suffer from severe numerical instability in some ranges of parameters of interest in applications. The application of these results is illustrated in the problem of performance approximation for the cumulative sum (CUSUM) quickest detection procedure
Keywords :
Poisson distribution; asymptotic stability; delay systems; delay-differential systems; numerical stability; stochastic processes; testing; CUSUM quickest detection procedure; Poisson processes; SPRT; asymptotic properties; average sample numbers; cumulative sum quickest detection procedure; delay-differential equations; error probabilities; exact numerically stable solutions; exit statistics; homogeneous Poisson processes; performance computation; sequential probability ratio test; sequential test; Control charts; Delay; Error probability; Performance analysis; Poisson equations; Sequential analysis; Statistics; Telecommunication traffic; Testing; Traffic control;
Journal_Title :
Information Theory, IEEE Transactions on
