Estimates of coefficient of overlapping
Calculates up to three estimates of activity pattern overlap based on times of observations for two species.
a vector of times of observations of species A in radians, ie. scaled to [0, 2π].
a vector of times of observations of species B in radians.
maximum value of k for optimal bandwidth estimation.
bandwidth adjustment; either a single value used for all 3 overlap estimates, or a vector of 3 different values; a NA value in
number of points at which to estimate density for comparison between species; smaller values give lower precision but run faster in simulations and bootstraps.
overlapTrue for the meaning of coefficient of overlapping, Δ.
These estimators of Δ use kernel density estimates fitted to the data to approximate the true density functions f(t) and g(t). Schmid & Schmidt (2006) propose five estimators of overlap:
Dhat1 is calculated from vectors of densities estimated at T equally-spaced times, t, between 0 and 2π:
For circular distributions, Dhat2 is equivalent to Dhat1, and Dhat3 is inapplicable.
Dhat4 and Dhat5 use vectors of densities estimated at the times of the observations of the species, x and y:
where n, m are the sample sizes and I is the indicator function (1 if the condition is true, 0 otherwise).
Returns a named vector of three estimates of overlap. Individual elements may be NA if the argument
adjust contained NAs. All will be NA if optimal bandwidth estimation failed.
Mike Meredith, based on work by Martin Ridout.
Ridout & Linkie (2009) Estimating overlap of daily activity patterns from camera trap data. Journal of Agricultural, Biological, and Environmental Statistics 14:322-337
Schmid & Schmidt (2006) Nonparametric estimation of the coefficient of overlapping - theory and empirical application, Computational Statistics and Data Analysis, 50:1583-1596.
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