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The general formula established for the conditional probability of the NHBP is nevertheless not tractable for practical applications. We can somewhat sacrifice the generality to obtain a more practical result, by defining a Markovian process with intensity at t that linearly depends on the value reached by the counting process at t‐. Such a linear dependency is shown to generate a counting process with a negative binomial distribution. This is called LEYP, which is the particular case of NHBP, for which the intensity linearly depends on N (t‐). The chapter then considers the conditional distribution of the number of events likely to occur in a given time interval, which the authors call prediction interval or prediction window, given the number of events that happened in a previous time interval. This conditional distribution is envisaged in increasingly general configurations. The chapter also investigates the limiting behavior of the distributions when 945.
The general formula established for the conditional probability of the NHBP is nevertheless not tractable for practical applications. We can somewhat sacrifice the generality to obtain a more practical result, by defining a Markovian process with intensity at t that linearly depends on the value reached by the counting process at t‐. Such a linear dependency is shown to generate a counting process with a negative binomial distribution. This is called LEYP, which is the particular case of NHBP, for which the intensity linearly depends on N (t‐). The chapter then considers the conditional distribution of the number of events likely to occur in a given time interval, which the authors call prediction interval or prediction window, given the number of events that happened in a previous time interval. This conditional distribution is envisaged in increasingly general configurations. The chapter also investigates the limiting behavior of the distributions when 945.
Linear Extension of the Yule Process
Le Gat, Yves (author)
2015-12-30
17 pages
Article/Chapter (Book)
Electronic Resource
English
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