pkernel {openCR} | R Documentation |
Kernel Distribution Functions
Description
Distribution of distance moved for each of the main movement kernels. Theoretical probability density, cumulative distribution function, and quantile function (inverse of the cumulative distribution function).
Usage
pkernel(q, movementmodel = c("BVN", "BVE", "BVC", "BVT", "RDE", "RDG", "RDL"),
move.a, move.b, truncate = Inf, lower.tail = TRUE)
dkernel(r, movementmodel = c("BVN", "BVE", "BVC", "BVT", "RDE", "RDG", "RDL"),
move.a, move.b, truncate = Inf)
qkernel(p, movementmodel = c("BVN", "BVE", "BVC", "BVT", "RDE", "RDG", "RDL"),
move.a, move.b, truncate = Inf, lower.tail = TRUE)
gkernel(r, movementmodel = c("BVN", "BVE", "BVC", "BVT", "RDE", "RDG", "RDL"),
move.a, move.b, truncate = Inf)
Arguments
p |
numeric vector of cumulative probabilities (0.5 for median) |
r |
numeric vector of distance moved |
q |
numeric vector of quantiles (distance moved) |
movementmodel |
character (see Movement models and openCR-vignette.pdf) |
move.a |
numeric parameter of movement kernel |
move.b |
numeric parameter of movement kernel |
truncate |
numeric q value at which distribution truncated |
lower.tail |
logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > x]. |
Details
Some formulae are given in openCR-vignette.pdf. gkernel
gives the 2-D probability density of the bivariate kernel g(r) = f(r) / (2\pi r)
; the remaining functions describe the distribution of distance moved f(r)
.
Computation of qkernel
for movementmodel = 'BVE'
uses
numerical root finding (function uniroot
).
Truncation (truncate = limit
for finite limit
) adjusts probabilities
upwards by 1/pkernel(limit,..., truncate = Inf) so that
pkernel(limit, ..., truncate = limit) equals 1.0.
By default the distribution is not truncated.
Value
For pkernel
–
Vector of cumulative probabilities corresponding to q. The cumulative probability is 1.0 for q > truncate.
For dkernel
–
Vector of probability density at radial distance r (zero for r > truncate).
For qkernel
–
Vector of quantiles (distances moved) corresponding to cumulative probabilities p.
For gkernel
–
Vector of 2-D probability density at radial distance r (zero for r > truncate).
References
Efford, M. G. and Schofield, M. R. (2022) A review of movement models in open population capture–recapture. Methods in Ecology and Evolution 13, 2106–2118. https://doi.org/10.1111/2041-210X.13947
See Also
Movement models, make.kernel
, matchscale
Examples
# plot 3 distributions chosen with matchscale to intersect at p = 0.5
q <- 0:100
plot(q, pkernel(q, 'BVN', 34), type = 'l', ylab = 'Cumulative probability')
lines(q, pkernel(q, 'BVT', move.a = 104, move.b = 5), col = 'darkgreen', lwd = 2)
lines(q, pkernel(q, 'BVT', move.a = 40, move.b = 1), col = 'orange', lwd = 2)
points(40, 0.5, pch = 16)
legend(62, 0.36, lty=1, lwd = 2, col = c('black','darkgreen','orange'),
legend = c('BVN sigma=34', 'BVT a=104, b=5', 'BVT a=40, b=1'))
# median
abline(v = qkernel(0.5, 'BVN', 34))