umvueLN: Computes UMVUEs of lognormal parameters
In Smisc: Sego Miscellaneous

Description Usage Arguments Details Value Author(s) References Examples

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

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

`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.

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

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

Landon Sego

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

# 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))