estimateParmsLognormFromSample {lognorm}

Estimate lognormal distribution parameters from a sample

Description

Estimate lognormal distribution parameters from a sample

Usage

estimateParmsLognormFromSample(x, na.rm = FALSE)

estimateStdErrParms(x, na.rm = FALSE)

Arguments

x

numeric vector of sampled values

na.rm

a logical value indicating whether NA values should be stripped before the computation proceeds.

Details

The expected value of a can be determined with higher accuracy the larger the sample. Here, the uncorrelated assumption is applied at the log scale and distribution parameters are returned with the same expected value as the sample, but with uncertainty (sigma) decreased by sqrt(nfin - 1).

Since with low relative error, the lognormal becomes very close to the normal distribution, the distribution of the mean can be well approximated by a normal with sd(mean(x)) ~ sd(x)/sqrt(n-1).

Value

numeric vector with components mu and sigma, i.e., the center parameter (mean at log scale, log(median)) and the scale parameter (standard deviation at log scale)

Functions

• estimateParmsLognormFromSample: Estimate lognormal distribution parameters from a sample

• estimateStdErrParms: Estimate parameters of the lognormal distribution of the mean from an uncorrelated sample

Examples

.mu <- log(1)
.sigma <- log(2)
n = 200
x <- exp(rnorm(n, mean = .mu, sd = .sigma))
exp(pL <- estimateParmsLognormFromSample(x)) # median and multiplicative stddev
c(mean(x), meanx <- getLognormMoments(pL["mu"],pL["sigma"])[,"mean"])
c(sd(x), sdx <- sqrt(getLognormMoments(pL["mu"],pL["sigma"])[,"var"]))

# stddev decreases (each sample about 0.9) to about 0.07
# for the mean with n replicated samples
se <- estimateStdErrParms(x)
sqrt(getLognormMoments(se["mu"],se["sigma"])[,"var"])
sd(x)/sqrt(n-1) # well approximated by normal
# expected value stays the same
c(meanx, getLognormMoments(se["mu"],se["sigma"])[,"mean"])