Calculate Lognormal Stochastic Matrix

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

Usage

calcLognormalKernel(distMat, meanlog, sdlog)

Arguments

distMat

Distance matrix from calcVinEll

meanlog

Log mean of Lognormal distribution

sdlog

Log standard deviation of Lognormal distribution

Details

The distribution and density functions for the lognormal kernel are given below: $$ F(x)=\frac{1}{2} + \frac{1}{2} \mathrm{erf}[\frac{\mathrm{ln}x-\mu}{\sqrt{2}\sigma}] $$ $$ f(x)=\frac{1}{x\sigma\sqrt{2\pi}}\mathrm{exp}\left( -\frac{(\mathrm{ln}x-\mu)^{2}}{2\sigma^{2}} \right) $$ where \(\mu\) is the mean on the log scale, and \(\sigma\) is the standard deviation on the log scale.

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 lognormal distribution over distances
#  mean and standard deviation are just for example
kernMat = calcLognormalKernel(distMat = distMat, meanlog = 100, sdlog = 10)