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

## 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

 `1` ```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

Landon Sego

## References

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```# 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)) ```

Smisc documentation built on Nov. 21, 2017, 9:02 a.m.