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eppminvmgf EPPM Probabilities
Computes the probabilities for an Extended Poisson Process Model by numerical inversion of a moment generating function.
lambda vector of positive birth rates. Missing values (NAs) are allowed but will usually produce an NA result.
second Logical variable. If second=T the second term correction to the saddlepoint approximation is included.
Numerical value giving the log-probability that N = n -1 where n = length(lambda).
The function computes the log-probability mass for the count distribution resulting from a pure birth process at unit time. The waiting time until the next birth is exponential with mean lambda[n], where n is the number of births so far. Let N be the number of births at unit time. The probability that N = n depends on lambda[0:n]. The function takes the input vector to be lambda[0:n] and computes log P(N=n).

The function computates the probabilities by numerically inverting a moment generating function using 400-point Guassian quadrature. The accuracy depends on how well the limit of integration is chosen.

The computation of probabilities for the pure birth process is central to extended Poisson process models for modelling count data.
Smyth, G. K., and Podlich, H. M. (2002). An improved saddlepoint approximation based on the negative binomial distribution for the general birth process. Computational Statistics 17, 17-28. [PDF]
Podlich, H. M., Faddy, M. J., and Smyth, G. K. (1999). Semi-parametric extended Poisson process models.
eppmsadno, eppmsadnb, eppmsadzc, S-Plus programs for EPPM by Heather Podlich.
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Gordon Smyth. Copyright © 1996-2016. Last modified: 10 February 2004