Title :
Least squares estimation of nonhomogeneous Poisson processes
Author :
Kuhl, Michael E. ; Damerdji, Halim ; Wilson, James R.
Author_Institution :
Dept. of Ind. & Manuf. Syst. Eng., Louisiana State Univ. Baton Rouge, LA, USA
Abstract :
We formulate and evaluate weighted and ordinary least squares procedures for estimating the parametric rate function of a nonhomogeneous Poisson process. Special emphasis is given to processes having an exponential rate function, where the exponent may include a polynomial component or some trigonometric components or both. Theoretical and experimental evidence is provided to explain some surprising problems with the weighted least squares procedure. The ordinary least squares procedure is based on a square root transformation of the “detrended” event times; and the results of an extensive Monte Carlo study are summarized to show the advantages and disadvantages of this procedure
Keywords :
Poisson distribution; least squares approximations; Monte Carlo study; event times; exponential rate function; least squares procedures; nonhomogeneous Poisson processes; ordinary least squares procedure; parametric rate function; polynomial component; square root; trigonometric components; Distribution functions; Industrial engineering; Industrial relations; Least squares approximation; Least squares methods; Manufacturing industries; Manufacturing systems; Parameter estimation; Polynomials; Systems engineering and theory;
Conference_Titel :
Simulation Conference Proceedings, 1998. Winter
Conference_Location :
Washington, DC
Print_ISBN :
0-7803-5133-9
DOI :
10.1109/WSC.1998.745045