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st: calculating poisson process (arrival rate)


From   Caleb Southworth <caleb.southworth@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: calculating poisson process (arrival rate)
Date   Tue, 13 Mar 2012 10:52:03 -0700

Dear Listers,

How can I compute a poisson process (arrival rate) for the cumulative
number of events Y(t)

where

Pr[Y(t+Dt) - Y(t) = 1 | Y(t) = y]/Dt

t is time

Dt is delta time or the time between changes in the arrival rate.

y is the count, y>=0

The variables at hand are the start time and finish time for each
event. From those I calculate the number of organizations in existence
and the number born each year. For exampe:

    | start   finish   count   born |
    |-------------------------------|
 1. |  1921     1921       1      1 |
 2. |  1922     1925       2      1 |
 3. |  1924     1926       4      2 |
 4. |  1924        .       4      2 |
 5. |  1936     1940       5      1 |
    |-------------------------------|
 6. |  1937        .       6      1 |
 7. |  1940        .       6      1 |
 8. |  1949     1950       7      1 |
 9. |  1950        .       7      1 |
10. |  1951        .       8      1 |


My current idea is to generate the probabilities with Scott Long's
prcounts (part of Spost), but perhaps there is some more direct
solution?

Any comments would be greatly appreciated.

Caleb Southworth
Univ. of Oregon Sociology

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