loadflex: Models and Tools for Watershed Flux Estimates

Description Usage Arguments Details Examples

logToLin makes the transformation from the moments of a lognormal distribution in log space to the moments of the same distribution in linear space.

linToLog makes the opposite transformation, from the moments of a lognormal distribution in linear space to the moments of the same distribution in log space.

mixedToLog transforms from a mixed pair - either meanlin and sdlog, or meanlog and sdlin - and returns meanlog and sdlog.

logToLin(meanlog, sdlog, mslist)

linToLog(meanlin, sdlin, mslist)

mixedToLog(meanlin, sdlog, meanlog, sdlin)

`meanlog`	The mean of the distribution on the log scale, with the same meaning as the `meanlog` argument to `rlnorm`.
`sdlog`	The standard deviation of the distribution on the log scale, with the same meaning as the `sdlog` argument to `rlnorm`.
`mslist`	Optionally, a list containing the meanlog and sdlog as the first and second elements. If this argument is specified, the first two arguments should be left missing.
`meanlin`	The mean of the lognormal distribution on the linear scale.
`sdlin`	The standard deviation of the lognormal distribution on the linear scale.

Terminology

Let L be a sample from a lognormal distribution in linear space; for example, L=rlnorm(1000) could be a set of predicted flux rates in kg/day. Then let N be the corresponding set of predictions in log space, as they emerge from a model with a logged term on the left-hand side; for example, the output of predict(lm(log(L_obs) ~ ...)) where L_obs is the set of observed flux rates used to calibrate the lm model. N is related to L by N=log(L) or L=exp(N), but the parameters of their distributions are more complicated.

(It could also be that L is not a set of predicted flux rates but simply the uncertainty distribution of a single flux rate prediction. The same principles apply.)

Given the above definition,

meanlin = mean(L) = mean(exp(N)) = exp(mean(N) + sd(N)^2/2)
sdlin = sd(L) = sd(exp(N)) = sqrt((exp(sd(N)^2) - 1) * exp(2*mean(N) + sd(N)^2))
meanlog = mean(N) = mean(log(L)) = log(mean(L)^2/sqrt(sd(L)^2 + mean(L)^2))
sdlog = sd(N) = sd(log(L)) = sqrt(log(1 + sd(L)^2/mean(L)^2))

Note that meanlin does NOT simply equal exp(mean(N)), and sdlin does NOT equal exp(sd(N)); this function exists to apply those more complicated expressions on the right in the above list. Specifically, this function helps you convert from meanlog=mean(N), sdlog=sd(N) to an appropriate mean and sd for L in linear space.

# Explore with draws from a lognormally distributed sample
library(ggplot2)
logparams <- list(meanlog = 1, sdlog = 0.5)
loglin_data <- data.frame(rlnorm=rlnorm(1000, meanlog=logparams$meanlog, sdlog=logparams$sdlog))
ggplot(loglin_data, aes(x=log(rlnorm))) + geom_density() + 
  geom_vline(xintercept=logparams$meanlog, color="red") + 
  geom_vline(xintercept=logparams$meanlog+c(-1,1)*logparams$sdlog, color="blue") 
linparams <- logToLin(ms=logparams)
ggplot(loglin_data, aes(x=rlnorm)) + geom_density() + 
  geom_vline(xintercept=linparams$meanlin, color="red") + 
  geom_vline(xintercept=linparams$meanlin+c(-1,1)*linparams$sdlin, color="blue") 
# 
# logToLin
logToLin(meanlog=1, sdlog=0.5)
logToLin(mslist=list(meanlog=1, sdlog=0.5))
logToLin(ms=linToLog(meanlin=3.080217, sdlin=1.641572))
#
# linToLog
linToLog(meanlin=1, sdlin=0.5)
linToLog(mslist=list(meanlin=1, sdlin=0.5))
linToLog(ms=logToLin(meanlog=-0.1115718, sdlog=0.4723807))
#
# mixedToLog
linparams <- data.frame(meanlin=1, sdlin=0.5)
logparams <- linToLog(ms=linparams)
mixedToLog(meanlin=linparams$meanlin, sdlog=logparams$sdlog)
## Not run: mixedToLog(meanlog=logparams$meanlog, sdlin=linparams$sdlin)
logToLin(ms=mixedToLog(meanlin=linparams$meanlin, sdlog=logparams$sdlog))