[GENERAL INFORMATION]
Function Name=ECS
Brief Description=Edgeworth-Cramer Peak Function for use in chromatography
Function Source=fgroup.ECS
Function Type=Built-in
Function Form=Expression
Number Of Parameters=6
Number Of Independent Variables=1
Number Of Dependent Variables=1


[FITTING PARAMETERS]
Naming Method=User-Defined
Names=y0,xc,A,w,a3,a4
Meanings=offset,center,amplitude,width,unknown,unknown
Lower Bounds=--,--,0.0(X,ON),0.0(X,ON),--,--
Upper Bounds=--,--,--,--,--,--
Number Of Significant Digits=


[FORMULA]

y=y0+A/(w*2*pi)*(exp(-0.5*((x-xc)/w)^2)*(1+(a3/(3*2*1))*((x-xc)/w)*(((x-xc)/w)^2-3)+(a4/(4*3*2*1))*(((x-xc)/w)^4-6*((x-xc)/w)^3+3)+((10*a3^2)/(6*5*4*3*2*1))*(((x-xc)/w)^6-15*((x-xc)/w)^4+45*((x-xc)/w)^2-15)))

[CONSTRAINTS]



[CONSTANTS]



[Parameters Initialization]
sort(x_y_curve);
//smooth(x_y_curve, 2);
y0 = yatxmin( x_y_curve );
w = 0.85 * fwhm( x_y_curve, y0 );
A = area( x_y_curve, y0 );
if ( A > 0 ) xc = xatymax( x_y_curve );
else xc = xatymin( x_y_curve );
a3 = 1.0;
a4 = 1.0;


[INITIALIZATIONS]



[AFTER FITTING]



[INDEPENDENT VARIABLES]
x=


[DEPENDENT VARIABLES]
y=


[CONTROLS]
General Linear Constraints=Off
Initialization Scripts=Off
Scripts After Fitting=Off
Number Of Duplicates=0
Duplicate Offset=2
Duplicate Unit=5
Peak Center=2
Peak Width=4
Peak Amplitude=3
