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Data Analysis and Statistics for Geography, Environmental Science, and Engineering
book

Data Analysis and Statistics for Geography, Environmental Science, and Engineering

by Miguel F. Acevedo
December 2012
Beginner content levelBeginner
557 pages
19h 5m
English
CRC Press
Content preview from Data Analysis and Statistics for Geography, Environmental Science, and Engineering
379Dependent Stochastic Processes and Time Series
as the sum of all the holding time densities corresponding to transitions out of state j. The mean
waiting time in role j is then the mean of W
j
(T), and denoted as M
j
,
j
i
ij
ij
M
p
j
==
=
1
4
12 4µ ,, ,
(11.20)
or the sum of all products of the probability p
ij
and the mean k
ij
/d
ij
of the h
ij
(t) density. In turn, the
mean time between transitions M is a weighted sum of the mean waiting times in each state
M
XM
j
j
j
=
=
1
4
*
(11.21)
where the weights used in the average are the stationary proportions of the embedded chain as given
in the previous section. The steady-state occupancy probabilities, and therefore the stationary pro-
portions X
**
i
for all the roles can be calculated as
jjj
XXMM
j
** *
,, ,
==
1
12 4
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Publisher Resources

ISBN: 9781439885017