calcHurdleExpKernel {MGDrivE} | R Documentation |
Calculate Zero-inflated Exponential Stochastic Matrix
Description
Given a distance matrix from calcVinEll
, calculate a
stochastic matrix where one step movement probabilities follow an zero-inflated
exponential density with a point mass at zero. The point mass at zero represents
the first stage of a two-stage process, where mosquitoes decide to stay at
their current node or leave anywhere. This parameter can be calculated from
lifetime probabilities to stay at the current node with the helper function
calcZeroInflation
.
Usage
calcHurdleExpKernel(distMat, rate, p0)
Arguments
distMat |
Distance matrix from |
rate |
Rate parameter of |
p0 |
Point mass at zero |
Details
If a mosquito leaves its current node, with probability 1-p_{0}
, it
then chooses a destination node according to a standard exponential density
with rate parameter rate
.
The distribution and density functions for the zero inflated exponential kernel are given below:
F(x)=p_{0}\theta(x) + (1-p_{0})(1-e^{-\lambda x})
f(x)=p_{0}\delta(x)+(1-p_{0})\lambda e^{-\lambda x}
where \lambda
is the rate parameter of the exponential distribution,
\theta(x)
is the Heaviside step function and \delta(x)
is the
Dirac delta function.
Examples
# setup distance matrix
# two-column matrix with latitude/longitude, in degrees
latLong = cbind(runif(n = 5, min = 0, max = 90),
runif(n = 5, min = 0, max = 180))
# Vincenty Ellipsoid distance formula
distMat = calcVinEll(latLongs = latLong)
# calculate hurdle exponential distribution over distances
# rate and point mass are just for example
kernMat = calcHurdleExpKernel(distMat = distMat, rate = 1/1e6, p0 = 0.1)