calcGammaKernel function

Calculate Gamma Stochastic Matrix

Given a distance matrix from calcVinEll, calculate a stochastic matrix where one step movement probabilities follow a gamma density.

calcGammaKernel(distMat, shape, rate)

Arguments

• distMat: Distance matrix from calcVinEll
• shape: Shape parameter of GammaDist distribution
• rate: Rate parameter of GammaDist distribution

Details

The distribution and density functions for the gamma kernel are given below:

where $\Gamma(\alpha)$ is the Gamma function, $\gamma(\alpha,\beta x)$ is the lower incomplete gamma function, and $\alpha,\beta$ are the shape and rate parameters, respectively.

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 gamma distribution over distances
#  shape and rate are just for example
kernMat = calcGammaKernel(distMat = distMat, shape = 1, rate = 1)