- Computes the probabilities for an Extended Poisson Process Model by numerical inversion
of a moment generating function.
- REQUIRED ARGUMENTS
||vector of positive birth rates. Missing values (NAs) are allowed but will usually
produce an NA result.
- OPTIONAL ARGUMENTS
||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.
- Podlich, H. M., Faddy, M. J., and Smyth, G. K. (1999). Semi-parametric extended Poisson
- SEE ALSO
- eppmsadno, eppmsadnb, eppmsadzc, S-Plus
programs for EPPM by Heather Podlich.
Copyright © 1996-2016. Last modified:
10 February 2004