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Plotting and nonlinear fitting software

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fit_equations

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Table of Contents

Predefined Fit Curves Equations

All predefined Fit Curves are listed in this table. You also can specify custom fit equation. Unlike custom fit equations these curves can be adjusted with mouse on Fit Plot.

Name Formula Additional Properties
Line y = a x + b
Parabola y = a x^2 + b x + c Vertex:
x_0 = − b / {2 a}
y_0 = c − {b^2} / {4 a}
Gaussian y = a exp(− ln(2) ({x−x_0}/dx)^2) Area:
S = sqrt{pi / {ln {2}}} ~ a dx
Standard deviation:
sigma = dx / sqrt{2 ln 2}
Gaussian-A
(normalized)
y = sqrt{{ln {2}} / pi} ~ a / dx exp(− ln(2) ({x−x_0}/dx)^2) Amplitude:
A = sqrt{{ln 2} / pi} ~ a/dx
Standard deviation:
sigma = dx / sqrt{2 ln 2}
Lorentzian y = a 1 / {1 + ({x−x_0} / dx)^2} Area:
S = pi a dx
Lorentzian-A
(normalized)
y = a / {pi dx} 1 / {1 + ({x−x_0} / dx)^2} Amplitude:
A = a / {pi dx}
Gauss Derivative y = − 2 ln(2) ~ {a (x−x_0)} / {dx^2} exp(− ln(2) ({x−x_0}/dx)^2) Area (second integral):
S = sqrt{pi / {ln {2}}} ~ a dx
Standard deviation:
sigma = dx / sqrt{2 ln 2}
Peak-to-peak horizontal:
p_x = sqrt{2/{ln {2}}} ~ dx
Peak-to-peak vertical:
p_y = 2 sqrt{{2 ln {2}} / e} ~ a / dx
Lorentz Derivative y=−2 a {x−x_0}/{dx^2} {(1 + ({x−x_0} / dx)^2)^{−2}} Area (second integral):
S = pi a dx
Peak-to-peak horizontal:
p_x = 2/{sqrt {3}} ~ dx
Peak-to-peak vertical:
p_y = {3 sqrt {3}} / 4 ~ a / dx

See Also

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fit_equations.1288061426.txt.gz · Last modified: Sun Nov 8 12:20:32 2015 (external edit)