deerlab.dd_rice3#

dd_rice3 = <deerlab.model.Model object>#

Sum of two 3D-Rice distributions model

Parameters:
rarray_like

Distance axis, in nanometers.

location1scalar

1st Rician location.

spread1scalar

1st Rician spread.

location2scalar

2nd Rician location.

spread2scalar

2nd Rician spread.

location3scalar

3rd Rician location.

spread3scalar

3rd Rician spread.

amp2scalar

2nd Rician amplitude.

amp1scalar

1st Rician amplitude.

amp3scalar

3rd Rician amplitude.

Returns:
Pndarray

Distance distribution.

Notes

Parameter List

Name

Lower

Upper

Type

Frozen

Unit

Description

location1

1

20

nonlin

No

nm

1st Rician location

spread1

0.05

2.5

nonlin

No

nm

1st Rician spread

location2

1

20

nonlin

No

nm

2nd Rician location

spread2

0.05

2.5

nonlin

No

nm

2nd Rician spread

location3

1

20

nonlin

No

nm

3rd Rician location

spread3

0.05

2.5

nonlin

No

nm

3rd Rician spread

amp2

0

inf

linear

No

2nd Rician amplitude

amp1

0

inf

linear

No

1st Rician amplitude

amp3

0

inf

linear

No

3rd Rician amplitude

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)

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=3 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.

Examples

Example of the model evaluated at the start values of the parameters:

(Source code, png, hires.png, pdf)

../_images/deerlab-dd_rice3-1.png