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April 18th, 2017, 02:15 AM   #1
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Inverse of sum of error functions

How to find the inverse function of
f(x)=sum_{i=0}^{4} Ai[1+erf((x-bi)/ci)]
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April 18th, 2017, 02:31 AM   #2
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Originally Posted by shriramtej View Post
How to find the inverse function of

$f(x) = \sum_{i=0}^{4} A_i \left[1+ erf\left(\dfrac{x - b_i}{c_i}\right)\right]$
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April 19th, 2017, 10:13 PM   #3
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The exact function is f(x)=sgn(x)\sqrt[d]{u\sum\limits_{i=1}^{4} \frac{\sqrt{\pi}a_i c_i}{2} [1+erf(\frac{|x|-b_i}{c_i})]} where d and u are positive constants. x is a complex random variable with magnitudes in the range [0,1]. The exact values are a1 = 0.19; b1 = 0.2512; c1 = 0.003164; a2 = 0.1; b2 = 0.1142; c2 = 0.006324; a3 = 0.14; b3 = 0.3322; c3 = 0.003054; a4 = 0.02778; b4 = 0.2211; c4 = 0.151;
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