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Fit Truncated Normal Distribution from Mode and 95% Confidence Intervals

Source: R/fit_truncnorm_from_ci.R
fit_truncnorm_from_ci.Rd

This function calculates the mean, sd, and truncation bounds of a truncated normal distribution that best matches a given mode and 95% confidence intervals.

Usage

fit_truncnorm_from_ci(
  mode_val,
  ci_lower,
  ci_upper,
  a = NULL,
  b = NULL,
  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.

a

Numeric. Lower truncation bound (default: -Inf).

b

Numeric. Upper truncation bound (default: Inf).

method

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

verbose

Logical. If TRUE, print diagnostic information.

Value

A list containing:

  • mean: The mean parameter (mu) of the underlying normal distribution

  • sd: The standard deviation parameter (sigma) of the underlying normal distribution

  • a: The lower truncation bound

  • b: The upper truncation bound

  • fitted_mean: The mean of the truncated distribution

  • fitted_ci: The 95% CI of the fitted truncated distribution

  • mode: The mode of the fitted truncated distribution

Details

For a truncated normal distribution:

  • The mode may differ from the mean due to truncation

  • If truncation is symmetric and far from the mean, the mode is close to the mean

  • Asymmetric truncation shifts the mode away from the mean

If truncation bounds are not specified, they are estimated from the CI, extending slightly beyond to allow for a proper truncated distribution.

Examples

# Example 1: Fit truncated normal with specified bounds
result <- fit_truncnorm_from_ci(mode_val = 0.5,
                                 ci_lower = 0.2,
                                 ci_upper = 0.8,
                                 a = 0, b = 1)
print(result)
#> $mean
#> [1] 0.5
#> 
#> $sd
#> [1] 0.127551
#> 
#> $a
#> [1] 0
#> 
#> $b
#> [1] 1
#> 
#> $fitted_mean
#> [1] 0.4989997
#> 
#> $fitted_ci
#> [1] 0.2500963 0.7499037
#> 
#> $mode
#> [1] 0.499617
#> 

# Example 2: Auto-detect truncation bounds
result <- fit_truncnorm_from_ci(mode_val = 5,
                                 ci_lower = 2,
                                 ci_upper = 8)