calcGammaKernel.RdGiven a distance matrix from calcVinEll, calculate a
stochastic matrix where one step movement probabilities follow a gamma density.
calcGammaKernel(distMat, shape, rate)
| distMat | Distance matrix from |
|---|---|
| shape | Shape parameter of |
| rate | Rate parameter of |
The distribution and density functions for the gamma kernel are given below: $$ F(x)=\frac{1}{\Gamma(\alpha)}\gamma(\alpha,\beta x) $$ $$ f(x)=\frac{\beta^{\alpha}}{\Gamma(\alpha)}x^{\alpha-1}e^{-\beta x} $$ 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.
# 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)