getParmsLognormForModeAndUpper: Calculate mu and sigma of lognormal from summary statistics.

In bgctw/lognorm: Functions for the Lognormal Distribution

Description

Calculate mu and sigma of lognormal from summary statistics.

Usage

getParmsLognormForMedianAndUpper(median, upper, sigmaFac = qnorm(0.99))

getParmsLognormForMeanAndUpper(mean, upper, sigmaFac = qnorm(0.99))

getParmsLognormForLowerAndUpper(lower, upper, sigmaFac = qnorm(0.99))

getParmsLognormForLowerAndUpperLog(lowerLog, upperLog, sigmaFac = qnorm(0.99))

getParmsLognormForModeAndUpper(mle, upper, sigmaFac = qnorm(0.99))

getParmsLognormForMoments(mean, var, sigmaOrig = sqrt(var))

getParmsLognormForExpval(mean, sigmaStar)

Arguments

median	geometric mu (median at the original exponential scale)
upper	numeric vector: value at the upper quantile, i.e. practical maximum
sigmaFac	sigmaFac=2 is 95% sigmaFac=2.6 is 99% interval.
mean	expected value at original scale
lower	value at the lower quantile, i.e. practical minimum
lowerLog	value at the lower quantile, i.e. practical minimum at log scale
upperLog	value at the upper quantile, i.e. practical maximum at log scale
mle	numeric vector: mode at the original scale
var	variance at original scale
sigmaOrig	standard deviation at original scale
sigmaStar	multiplicative standard deviation

Details

For getParmsLognormForMeanAndUpper there are two valid solutions, and the one with lower sigma , i.e. the not so strongly skewed solution is returned.

Value

numeric matrix with columns 'mu' and 'sigma', the parameter of the lognormal distribution. Rows correspond to rows of inputs.

Functions

• getParmsLognormForMedianAndUpper: Calculates mu and sigma of lognormal from median and upper quantile.

• getParmsLognormForMeanAndUpper: Calculates mu and sigma of lognormal from mean and upper quantile.

• getParmsLognormForLowerAndUpper: Calculates mu and sigma of lognormal from lower and upper quantile.

• getParmsLognormForLowerAndUpperLog: Calculates mu and sigma of lognormal from lower and upper quantile at log scale.

• getParmsLognormForModeAndUpper: Calculates mu and sigma of lognormal from mode and upper quantile.

• getParmsLognormForMoments: Calculate mu and sigma from moments (mean anc variance)

• getParmsLognormForExpval: Calculate mu and sigma from expected value and geometric standard deviation

References

Limpert E, Stahel W & Abbt M (2001) Log-normal Distributions across the Sciences: Keys and Clues. Oxford University Press (OUP) 51, 341, 10.1641/0006-3568(2001)051[0341:lndats]2.0.co;2

Examples

# example 1: a distribution with mode 1 and upper bound 5
(thetaEst <- getParmsLognormForModeAndUpper(1,5))
mle <- exp(thetaEst[1] - thetaEst[2]^2)
all.equal(mle, 1, check.attributes = FALSE)

# plot the distributions
xGrid = seq(0,8, length.out = 81)[-1]
dxEst <- dlnorm(xGrid, meanlog = thetaEst[1], sdlog = thetaEst[2])
plot( dxEst~xGrid, type = "l",xlab = "x",ylab = "density")
abline(v = c(1,5),col = "gray")

# example 2: true parameters, which should be rediscovered
theta0 <- c(mu = 1, sigma = 0.4)
mle <- exp(theta0[1] - theta0[2]^2)
perc <- 0.975		# some upper percentile, proxy for an upper bound
upper <- qlnorm(perc, meanlog = theta0[1], sdlog = theta0[2])
(thetaEst <- getParmsLognormForModeAndUpper(
  mle,upper = upper,sigmaFac = qnorm(perc)) )

#plot the true and the rediscovered distributions
xGrid = seq(0,10, length.out = 81)[-1]
dx <- dlnorm(xGrid, meanlog = theta0[1], sdlog = theta0[2])
dxEst <- dlnorm(xGrid, meanlog = thetaEst[1], sdlog = thetaEst[2])
plot( dx~xGrid, type = "l")
#plot( dx~xGrid, type = "n")
#overplots the original, coincide
lines( dxEst ~ xGrid, col = "red", lty = "dashed")

# example 3: explore varying the uncertainty (the upper quantile)
x <- seq(0.01,1.2,by = 0.01)
mle = 0.2
dx <- sapply(mle*2:8,function(q99){
  theta = getParmsLognormForModeAndUpper(mle,q99,qnorm(0.99))
  #dx <- dDistr(x,theta[,"mu"],theta[,"sigma"],trans = "lognorm")
  dx <- dlnorm(x,theta[,"mu"],theta[,"sigma"])
})
  matplot(x,dx,type = "l")
# Calculate mu and sigma from expected value and geometric standard deviation
.mean <- 1
.sigmaStar <- c(1.3,2)
(parms <- getParmsLognormForExpval(.mean, .sigmaStar))
# multiplicative standard deviation must equal the specified value
cbind(exp(parms[,"sigma"]), .sigmaStar)

bgctw/lognorm documentation built on March 17, 2021, 3:21 a.m.