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 parameter of GammaDist distribution Rate parameter of GammaDist distribution

## Details

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.

## 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)