calcGammaKernel {MGDrivE}

Calculate Gamma Stochastic Matrix

Description

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

Usage

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:

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)