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Estimating the intensity function of the nonstationary poisson process

University of British Columbia

Let{N(t), -T<t<T} be a nonstationary Poisson process with intensity function, λ(t)>0, assumed integrable on [-T,T]. The optimal linear estimator, λ[sub L], of the intensity function is considered in this thesis. Chapter 1 discusses λ[sub L] as a function of h(t;s), which is Lthe unique solution of the Fredholm integral equation of the second kind, m(s)h[sub t](s) + /[sup b/ sub a]K(s;u)h[sub t](u)du = K(t;s), a<s<b. Chapters 2 and 3 are respectively devoted to a discussion of some of the exact and approximate methods for solving the above integral equation. To illustrate the use of the techniques devised, three numerical examples are treated. Chapter 4 deals with data on oilwell discoveries in Alberta, Canada. Finally, in Chapter 5, the model is applied to data on traffic counts on the Lions Gate Bridge, Vancouver, and to data on coal-mining disasters in Great Britain. Computer programs and numerous diagrams are also presented.

Text

2010-02-11

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http://hdl.handle.net/2429/20061

Mathematics

University of British Columbia

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