calcLognormalKernel.RdGiven a distance matrix from calcVinEll,
calculate a stochastic matrix where one step movement probabilities follow a lognormal density.
calcLognormalKernel(distMat, meanlog, sdlog)
| distMat | Distance matrix from |
|---|---|
| meanlog | Log mean of |
| sdlog | Log standard deviation of |
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.
# 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)