# 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.