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This might be a stupid question, but whenever I encounter the sigmoid function, it is written like this:

sigmoid

Is there any particular reason why it is (it seems to me) never mentioned in the form:

sigmoid alternative

This second form is the one I obtained from inverting the logit function myself and is just as valid. Is this just a matter of convention or am I missing something?

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    $\begingroup$ A guess: there's a general "preference" in mathematics for positive numbers over negative, and for positive values of $x$, the 1 term dominates the $e^{-x}$, so we list the most significant term first. $\endgroup$ – Nate Eldredge Jan 26 '17 at 17:06
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    $\begingroup$ Could it possibly be because the second form might raise doubt as to whether the '+ 1' bit is part of the exponent of e when you write it down sloppily? $\endgroup$ – Asciiom Jan 26 '17 at 17:07
  • $\begingroup$ That is actually a great point. When some people write fractions, the numerator and denominator can be quite small (not in value but in appearance). So writing the $1$ first would certainly eliminate that confusion of the $1$ being in the exponent. My original thinking was in line with Nate Eldredge's answer, but this point is also quite valid. $\endgroup$ – Dave Jan 26 '17 at 17:12
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    $\begingroup$ @JeroenMoons I think you're probably spot-on, and now it just 'looks' right, since we are all used to it. $\endgroup$ – The Count Jan 26 '17 at 17:19
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Best reason I could think of seems plausible: because the second form might raise doubt as to whether or not the '+ 1' bit is part of the exponent of e when you write it down sloppily.

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