28.1.123 PearsonIV

Function

y=y_0+Ak\left[1+\left(\frac{x-\lambda\!}{\alpha\!}\right)\right]^{-m}e^{-v\tan^{-1}\left(\frac{x-\lambda\!}{\alpha\!}\right) }~~~~~ \left(m>\frac{1}{2}\right)

where k=\frac{2^{2m-2}|\Gamma\!\left(m+iv/2\right)|^2}{\pi\!\alpha\!\Gamma\!\left(2m-1\right)}

Brief Description

Pearson Type IV distribution for negative discriminant, suited to model pull distributions.

Sample Curve

PearsonIV.png

Parameters

Number: 6

Names: y0, A, m, v, alpha, lam

Meanings: y0=offset, A =area, m = unknown, v = unknown, alpha = x width, lam = x center

Lower Bounds: m > 0.5

Upper Bounds: none

Script Access

y = nlf_pearsoniv(x, y0, A, m, v, alpha, lam)

Function File

FITFUNC\PEARSONIV.FDF

Category

Peak Functions, Statistics