twCoefLnormMLE: twCoefLnormMLE

In twDEMC: parallel DEMC

Description

Calculates mu and sigma of the lognormal distribution from mode and upper quantile.

Usage

twCoefLnormMLE(mle, quant, sigmaFac = qnorm(0.99))

Arguments

mle	numeric vector: mode at the original scale
quant	numeric vector: value at the upper quantile, i.e. practical maximum
sigmaFac	sigmaFac=2 is 95% sigmaFac=2.6 is 99% interval

Value

numeric matrix: columns mu and sigma parameter of the lognormal distribution. Rows correspond to rows of mle and quant

Author(s)

Thomas Wutzler

See Also

twQuantiles2Coef transOrigPopt.default

Examples

# example 1: a distribution with mode 1 and upper bound 5
(thetaEst <- twCoefLnormMLE(1,5))
all.equal( mle <- exp(thetaEst[1] -thetaEst[2]^2), 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
quant <- qlnorm(perc, meanlog=theta0[1], sdlog=theta0[2])
(thetaEst <- twCoefLnormMLE(mle,quant=quant,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")
lines( dxEst ~ xGrid, col="blue")	#overplots the original, coincide

# 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 = twCoefLnormMLE(mle,q99,qnorm(0.99))
		dx <- dDistr(x,theta[,"mu"],theta[,"sigma"],trans="lognorm")
	})
matplot(x,dx,type="l")

twDEMC documentation built on May 2, 2019, 5:38 p.m.