Exponentially Modified Gaussian

An exponentially modified Gaussian distribution is often encountered in modelling chromatographic peaks. The general form of the equation is given below.

$f(x)=y_{0}+{\frac {A}{t_{0}}}\left({\frac {1}{2}}\left({\frac {w}{t_{0}}}\right)^{2}-{\frac {x-x_{c}}{t_{0}}}\right)\int _{-\infty }^{z}{\frac {1}{\sqrt {2}}}exp\left({\frac {-y^{2}}{z}}\right)dy$

or

$f(x)=y_{0}+{\frac {A}{t_{0}}}\left({\frac {1}{2}}\left({\frac {w}{t_{0}}}\right)^{2}-{\frac {x-x_{c}}{t_{0}}}\right)\left({\frac {1}{2}}+{\frac {1}{2}}erf\left({\frac {z}{\sqrt {2}}}\right)\right)$

$y_{0}$ = the initial value

$A$ = the amplitude

$x_{c}$ = is the center of the peak

$w$ = the width of the peak

$t_{0}$ = the modification factor

$z={\frac {x-x_{c}}{w}}-{\frac {w}{t_{0}}}$

$erf\left({\frac {z}{\sqrt {2}}}\right)$ = the error function

References