umvueLN: Computes UMVUEs of lognormal parameters

Description Usage Arguments Details Value Author(s) References Examples

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

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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.

Details

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

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

Author(s)

Landon Sego

References

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

Examples

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# 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))


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