Two-part normal key function

The two-part normal detection function of Becker and Christ (2015). Either side of an estimated apex in the distance histogram has a half-normal distribution, with differing scale parameters. Covariates may be included but affect both sides of the function.

Usage

keyfct.tpn(distance, ddfobj)

Arguments

distance

perpendicular distance vector

ddfobj

meta object containing parameters, design matrices etc

Value

a vector of probabilities that the observation were detected given they were at the specified distance and assuming that g(mu)=1

Details

Two-part normal models have 2 important parameters:

• The apex, which estimates the peak in the detection function (where g(x)=1). The log apex is reported in summary results, so taking the exponential of this value should give the peak in the plotted function (see examples).

• The parameter that controls the difference between the sides .dummy_apex_side, which is automatically added to the formula for a two-part normal model. One can add interactions with this variable as normal, but don't need to add the main effect as it will be automatically added.

References

Becker, E. F., & Christ, A. M. (2015). A Unimodal Model for Double Observer Distance Sampling Surveys. PLOS ONE, 10(8), e0136403. doi:10.1371/journal.pone.0136403

Author

Earl F Becker, David L Miller