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Estimate Spreading Parameter from Narrow Standard

Source: R/step_sec_band_broadening.R
estimate_sigma.Rd

Estimates the instrumental spreading parameter (sigma) from a narrow molecular weight standard peak. This sigma value can then be used in step_sec_band_broadening() to correct for band broadening.

Usage

estimate_sigma(peak, method = c("gaussian", "fwhm", "moments"))

Arguments

peak

A measure_tbl or data frame with location and value columns representing a chromatographic peak from a narrow MW standard.

method

Method for sigma estimation:

  • "gaussian" (default): Fit a Gaussian and extract sigma

  • "fwhm": Calculate from full width at half maximum (sigma = FWHM / 2.355)

  • "moments": Calculate from second moment of the peak

Value

A list with components:

sigma

The estimated spreading parameter (Gaussian std dev)

tau

Exponential tail parameter (for EMG model), NA if not applicable

fwhm

Full width at half maximum

asymmetry

Peak asymmetry factor (> 1 indicates tailing)

method

The method used for estimation

Details

The spreading parameter sigma represents the standard deviation of the instrumental broadening function, assumed to be approximately Gaussian.

For best results, use a narrow polydispersity standard (PDI < 1.05) run under the same conditions as your samples.

Method Details:

  • gaussian: Fits a Gaussian function to the peak using nonlinear least squares. Most accurate for symmetric peaks.

  • fwhm: Uses the relationship sigma = FWHM / 2.355 for a Gaussian. Fast and robust but assumes symmetric peak.

  • moments: Calculates sigma from the second central moment. Accounts for asymmetry but sensitive to baseline.

Examples

if (FALSE) { # \dontrun{
# From a measure_tbl
sigma_result <- estimate_sigma(narrow_standard_peak)
sigma_result$sigma

# Use in band broadening correction
rec <- recipe(~., data = sec_data) |>
  step_sec_band_broadening(sigma = sigma_result$sigma)
} # }