probnzeros returns probability of zero bycatch in a specified number
of effort units, given bycatch per unit effort and dispersion index.
probnzeros(n, bpue, d)a vector of positive integers. Observed effort levels (in terms of effort units, e.g., trips or sets) for which to calculate probability of zero bycatch.
a positive number. Bycatch per unit effort.
a number greater than or equal to 1. Dispersion
index. The dispersion index corresponds to the variance-to-mean
ratio of effort-unit-level bycatch, so d = 1 corresponds to Poisson-
distributed bycatch, and d > 1 corresponds to overdispersed bycatch.
Vector of same length as n with probabilities of zero bycatch.
Returned invisibly
Calculated from the probability density at zero of the corresponding Poisson
(d = 1) or negative binomial (d > 1) distribution.
Caveat: probnzeros assumes that (1) observer coverage is
representative, (2) bycatch (bpue) is in terms of individuals (not
weight) per unit effort, and (3) the specified dispersion index reflects
the highest level of any hierarchical variance (e.g., using dispersion index
at trip level if greater than that at set level). Violating these assumptions
will likely result in negatively biased projections of the probability of
observing zero bycatch at a given level of observer coverage. More conservative
projections can be obtained by using a higher dispersion index d. Users
may want to explore uncertainty in dispersion index and in bycatch per unit
effort by varying those inputs.