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Fit Lognormal Distribution from Mode and 95% Confidence Intervals

Source: R/fit_lognormal_from_ci.R
fit_lognormal_from_ci.Rd

This function calculates the meanlog and sdlog parameters of a lognormal distribution that best matches a given mode and 95% confidence intervals.

Usage

fit_lognormal_from_ci(
  mode_val,
  ci_lower,
  ci_upper,
  method = "moment_matching",
  verbose = FALSE
)

Arguments

mode_val

Numeric. The mode of the distribution.

ci_lower

Numeric. The lower bound of the 95% confidence interval.

ci_upper

Numeric. The upper bound of the 95% confidence interval.

method

Character. Method to use: "moment_matching" (default) or "optimization".

verbose

Logical. If TRUE, print diagnostic information.

Value

A list containing:

  • meanlog: The mean of the logarithm (mu) of the lognormal distribution

  • sdlog: The standard deviation of the logarithm (sigma) of the lognormal distribution

  • mean: The mean of the distribution (not meanlog)

  • sd: The standard deviation of the distribution (not sdlog)

  • fitted_ci: The 95% CI of the fitted distribution

  • mode: The mode of the fitted distribution

Details

For a lognormal distribution with parameters meanlog (\(\mu\)) and sdlog (\(\sigma\)):

  • Mode = \(\exp(\mu - \sigma^2)\)

  • Mean = \(\exp(\mu + \sigma^2/2)\)

  • Variance = \((\exp(\sigma^2) - 1) \exp(2\mu + \sigma^2)\)

The moment matching method (default) matches the 95% CI exactly on the log scale: a lognormal is fully determined by two quantiles, so meanlog is the midpoint of log(ci_lower) and log(ci_upper) and sdlog is their distance divided by 2 * qnorm(0.975). mode_val is validated but does not move the fit; the implied mode exp(meanlog - sdlog^2) is returned as mode. Anchoring on a sample-based mode (for example a KDE mode of posterior draws) and then adding sdlog^2 shifted wide CIs upward by orders of magnitude, which is why the CI is authoritative here.

The optimization method fits meanlog and sdlog jointly to the mode and both quantiles, with all errors measured on the log scale and the mode weighted 10x; use it when mode_val is a trusted anchor.

Examples

# Example 1: Fit lognormal distribution
result <- fit_lognormal_from_ci(mode_val = 1,
                                 ci_lower = 0.5,
                                 ci_upper = 3)
print(result)
#> $meanlog
#> [1] 0.2027326
#> 
#> $sdlog
#> [1] 0.4570899
#> 
#> $mean
#> [1] 1.35961
#> 
#> $sd
#> [1] 0.6553832
#> 
#> $fitted_ci
#> [1] 0.5 3.0
#> 
#> $mode
#> [1] 0.9938206
#> 

# Example 2: Using optimization method
result <- fit_lognormal_from_ci(mode_val = 10,
                                 ci_lower = 2,
                                 ci_upper = 50,
                                 method = "optimization")