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An exponentially modified Gaussian distribution is often encountered in modelling chromatographic peaks.[ 1] [ 2] , [ 3]
f
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)
=
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+
A
t
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e
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p
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2
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w
t
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2
−
x
−
x
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t
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∫
−
∞
z
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2
e
x
p
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−
y
2
z
)
d
y
{\displaystyle f(x)=y_{0}+{\frac {A}{t_{0}}}exp\left({\frac {1}{2}}\left({\frac {w}{t_{0}}}\right)^{2}-{\frac {x-x_{c}}{t_{0}}}\right)\int _{-\infty }^{z}{\frac {1}{\sqrt {2}}}exp\left({\frac {-y^{2}}{z}}\right)dy}
or
f
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x
)
=
y
0
+
A
t
0
e
x
p
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2
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w
t
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)
2
−
x
−
x
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1
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e
r
f
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z
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)
{\displaystyle f(x)=y_{0}+{\frac {A}{t_{0}}}exp\left({\frac {1}{2}}\left({\frac {w}{t_{0}}}\right)^{2}-{\frac {x-x_{c}}{t_{0}}}\right)\left({\frac {1}{2}}+{\frac {1}{2}}erf\left({\frac {z}{\sqrt {2}}}\right)\right)}
y
0
{\displaystyle y_{0}}
A
{\displaystyle A}
x
c
{\displaystyle x_{c}}
w
{\displaystyle w}
t
0
{\displaystyle t_{0}}
t
0
>
0
{\displaystyle t_{0}>0}
z
=
x
−
x
c
w
−
w
t
0
{\displaystyle z={\frac {x-x_{c}}{w}}-{\frac {w}{t_{0}}}}
e
r
f
(
z
2
)
{\displaystyle erf\left({\frac {z}{\sqrt {2}}}\right)}
error function
References
