Distribution Shapes

For model based Fitting a variety of defined distribution shapes are available. Often there are several definitions of "width" (for example a Gaussian can be defined with a width of sigma, 2x sigma, FWHH(=FWHM), HWHH, etc.).

There is no reason to believe that a distribution between two spin labels on a protein should fit any of these lineshapes. All model based fitting is a simplification, of course.

Gaussian

The width is defined as FWHH, i.e. the distance between the two location where the amplitude is half the maximum.

(The statistician definition (via standard deviation) is different but can be derived, of course: FWHH ~ 2.355 * sigma)

Rice 3D

The statistical distribution of all distances between two 3D Gaussian clouds of points with a given sigma, and r is distance between the two centers. (reference)

( For large distance/width ratios a rice distribution will asymptotically have a Gaussian shape)

Cosine

The width is defined as FWHH, i.e. the distance between the two location where the amplitude is half the maximum.

(Similar to a Gaussian with the advantage that it drops to zero at a finite distance)

Circle

The width is defined as Base Width, i.e. the distance between the two location bracketing the distribution.

(Actually a half-ellipse, but the math is the same. Also drops to zero quickly.)

Square

The width is defined as the distance between the two location where the signal is vertical.

(Actually a rectangle (but can always be scaled to be a square). Equal distribution over the width of the line, zero outside).

Triangle

The width is defined as FWHH, i.e. the distance between the two location where the amplitude is half the maximum.

(An  Isosceles triangle, symmetric about the peak.).

Lorentzian

The width is defined as FWHH, i.e. the distance between the two location where the amplitude is half the maximum.

Pake

The width is defined as the splitting, i.e. the distance between the two location where the amplitude is maximal.

(While the peaks are infinitely narrow and infinitely high, the calculation is careful to give a best possible finite approximation).

Line Pair

The width is defined as the splitting, i.e. the distance between the two location.

(While the peaks are infinitely narrow and infinitely high, the calculation is careful to give an best possible finite approximation, proportionally filling two adjacent array bins according to the fractional position.)