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Chapter 11. Poisson processes.
Manual for SOA Exam MLC.
Chapter 11. Poisson processes.
Section 11.3. Interarrival times.
c 2008. Miguel A. Arcones. All rights reserved.
Extract from:
"Arcones' Manual for SOA Exam MLC. Fall 2009 Edition",
available at http://www.actexmadriver.com/
c 2008. Miguel A. Arcones. All rights reserved. Manual for SOA Exam MLC.
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Chapter 11. Poisson processes. Section 11.3. Interarrival times.
Arrival time
For n 1, let Sn be the arrival time of the n­th event, i.e.
Sn = inf{t 0 : N(t) = n}.
Notice that N(Sn) = n and N(t) < n, for t < Sn.
c 2008. Miguel A. Arcones. All rights reserved. Manual for SOA Exam MLC.
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Chapter 11. Poisson processes. Section 11.3. Interarrival times.
An useful relation between N(t) and Sn is

Source: Arcones, Miguel A. - Department of Mathematical Sciences, State University of New York at Binghamton

Collections: Mathematics