calcGammaKernel: Calculate Gamma Stochastic Matrix

In MGDrivE: Mosquito Gene Drive Explorer

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}{Γ(α)}γ(α,β x)

f(x)=\frac{β^{α}}{Γ(α)}x^{α-1}e^{-β x}

where Γ(α) is the Gamma function, γ(α,β x) is the lower incomplete gamma function, and α,β 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)

MGDrivE documentation built on Oct. 23, 2020, 7:28 p.m.