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 |

`x` |
Vector of lognormal data |

`tol` |
Tolerence level for convengence of the infinite series, |

`verbose` |
Logical indicating whether iteration steps for convergence of |

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.

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))
``` |

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