getParmsLognormForMedianAndUpper {lognorm}

Calculate mu and sigma of lognormal from summary statistics.

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)