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Suppose one has some data that looks exponentially distributed. Most, if not all, numerical subroutines can make the fit using least squares fitting of the function

\begin{equation} A\exp(-Bx), \end{equation}

where $A,B$ are the parameters of the fit. What happens if instead one has to fit

\begin{equation} A\exp(-B|x|), \end{equation}

and the empirical data is not symmetric about zero? Is it correct to say that there exists two sets of fitting parameters for $x\geq0$ and $x<0$?

user2820579
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    If you used different pairs of parameters for $\ x\ge0\ $ and $\ x<0\ $ you wouldn't be fitting the function $\ A\exp(-B|x|)\ $ to your data, but a different function $$ \cases{A_1\exp\left(B_1x\right)& for $\ x<0\ $\ A_2\exp\left(-B_2x\right)& for $\ x\ge0\ .$} $$ – lonza leggiera May 03 '20 at 01:38
  • Do you know how to do this for |x| and only one pair of parameters? – user2820579 May 03 '20 at 02:40
  • Just use a normal curve-fitting algorithm. However, if your empirical data is very far from symmetric about the origin, you gave no hope of getting a close fit, regardless of what you do. – lonza leggiera May 03 '20 at 04:13
  • I see. Thanks for the advice. – user2820579 May 03 '20 at 18:01

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