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

 1 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

  1 2 3 4 5 6 7 8 9 10 11 # 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.