dd_rice4

Sum of four 3D-Rice distributions

Syntax

info = dd_rice4()
P = dd_rice4(r,param)
Parameters
  • r - Distance axis (N-array)
  • param - Model parameters
Returns
  • P - Distance distribution (N-array)
  • info - Model information (struct)

Model

P(r) = a_1 R(r,\nu_1,\sigma_1) + a_2 R(r,\nu_2,\sigma_2) + a_3 R(r,\nu_3,\sigma_3) + (1-a_1-a_2-a_3) R(r,\nu_4,\sigma_4)

R(r,\nu,\sigma) = \frac{\nu^{n/2-1}}{\sigma^2}r^{n/2}\exp\left(-\frac{(r^2+\nu^2)}{2\sigma^2}\right)I_{n/2-1}\left(\frac{r\nu}{\sigma^2} \right)

where n=4 and I_{n/2-1}(x) is the modified Bessel function of the first kind with order n/2-1. This is a three-dimensional non-central chi distribution, the 3D generalization of the 2D Rice distribution.

Variable Symbol Default Lower Upper Description
param(1) \left<r_1\right> 2.5 1.0 20 center, 1st component
param(2) \sigma_1 0.7 0.1 5 width, 1st component
param(3) a_1 0.25 0 1 amplitude, 1st component
param(4) \left<r_2\right> 3.5 1.0 20 center, 2nd component
param(5) \sigma_2 0.7 0.1 5 width, 2nd component
param(6) a_2 0.25 0 1 amplitude, 2nd component
param(7) \left<r_3\right> 4.5 1.0 20 center, 3rd component
param(8) \sigma_3 0.7 0.1 5 width. 3rd component
param(9) a_3 0.25 0 1 amplitude, 3rd component
param(10) \left<r_3\right> 5.5 1.0 20 center, 4th component
param(11) \sigma_3 0.7 0.1 5 width. 4th component

Example using default parameters:

../_images/model_dd_rice4.png

Description

info = dd_rice4()

Returns an info structure containing the specifics of the model:

  • info.model - Full name of the parametric model.
  • info.nparam - Total number of adjustable parameters.
  • info.parameters - Structure array with information on individual parameters.
P = dd_rice4(r,param)

Computes the distance distribution model P from the axis r according to the parameters array param. The required parameters can also be found in the info structure.