pinvGauss: Inverse Gaussian distribution
In BruceKendall/PVA: Population viability analysis in R

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Cumulative distribution function for the inverse Gaussian distribution, for use with count-based density-independent PVA.

1	pinvGauss(T, mu, s2, d)

`T`	Time point(s) at which to evaluate the distribution. May be a vector.
`mu`	Mean growth rate of the population.
`s2`	Variance of the population growth rate.
`d`	Natural log of the ratio of starting population size to quasi-extinction population size. In the language of Morris and Doak (2002), d = log(Nc) - log(Nx).

Calculates the cumulative distribution function for the inverse Gaussian distribution, using the parameterization of Eq. (3.5) in Morris and Doak (2002). It is equivalent to the Matlab program extcdf.m on p. 80 of that book. This can be interpreted as the probability of quasi-extinction by a given time for a population exhibiting density-independent growth with the mean and variance of the instantaneous growth rate, r = log(lambda), given by mu and s2. See Chapt. 3 of Morris and Doak for details.

A vector of the same length as T, containing the CDF of the inverse Gaussian distribution at each value of T.

This differs from the inverse Gaussian distributions in the statmod and SuppDists libraries, not only in the parameterization, but also in that it allows evaluation of the incomplete inverse Gaussian distribution (the integral of the pdf is less than 1) that occurs when mu > 0.

Bruce E. Kendall (kendall@bren.ucsb.edu)

Morris, W. F. and Doak D. F. (2002) Quantitative Conservation Biology: Theory and Practice of Population Viability Analysis. Sunderland: Sinauer Associates.

count.DI.PVA

## Load the grizzly bear data
data(grizzly)

## Calculate the log-growth rates, and calculate their mean and variance
r <- log(grizzly$N[-1]/grizzly$N[-39])
mu <- mean(r); s2 <- var(r)

## Calculate the cumulative quasi-extinction risk (with threshold at 20) at
##  years 1-100
pinvGauss(1:100, mu, s2, log(grizzly$N[39]/20))