ON ESTIMATION OF POISSON INTENSITY FUNCTIONS

ROELOF HELMERS^{1} AND RIČARDAS ZITIKIS^{2}

1Centre for Mathematics and Computer Science, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands 2Laboratory for Research in Statistics and Probability, Carleton University, 1125 Colonel By Drive, Ottawa, Canada K1S 5B6

(Received June 26, 1996; revised October 13, 1997)

Abstract. Under the presence of only one realization, we consider a computationally simple algorithm for estimating the intensity function of a Poisson process with exponential quadratic and cyclic of fixed frequency trends. We argue that the algorithm can successfully be used to estimate any Poisson intensity function provided that it has a parametric form.

Key words and phrases: Poisson process, point process, linear Poisson process, modulated Poisson process.