Smisc (version 0.3.9.1)

umvueLN: Computes UMVUEs of lognormal parameters

Description

Computes uniformly minimum variance unbiased (UMVU) estimates of the mean, the standard error of the mean, and the standard deviation of lognormally distributed data.

Usage

umvueLN(x, tol = 1e-15, verbose = FALSE)

Arguments

x

Vector of lognormal data

tol

Tolerence level for convengence of the infinite series, Psi. Convergence occurs when the absolute value of the current term in the series is less than tol.

verbose

Logical indicating whether iteration steps for convergence of Psi are printed.

Value

Returns a named vector with the following components

mu

The UMVUE of the mean

se.mu

The UMVUE standard error of the mean

sigma

The UMVUE of the standard deviation

Details

Calculates equations 13.3, 13.5, and 13.6 of Gilbert (1987).

References

Gilbert, Richard O. (1987) Statistical Methods for Environmental Pollution Monitoring, John Wiley & Sons, Inc. New York, pp 164-167.

Examples

# NOT RUN {
# Test from Gilbert 1987, Example 13.1, p 166
x <- c(3.161, 4.151, 3.756, 2.202, 1.535, 20.76, 8.42, 7.81, 2.72, 4.43)
y <- umvueLN(x)
print(y, digits = 8)

# Compare to results from PRO-UCL 4.00.02:

# MVU Estimate of Mean                     5.6544289
# MVU Estimate of Standard Error of Mean   1.3944504
# MVU Estimate of SD                       4.4486438

# Compare these to Gilbert's printed results (which have rounding error)
Gilbert <- c(5.66, sqrt(1.97), sqrt(19.8))
print(round(abs(y - Gilbert), 2))
# }