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Dec 8, 2015 at 22:26 comment added Glen_b @Mitch They are! The probit link function is often used in place of the logit in Bernoulli(/binomial) glms, for example (and it's not the only one; many stats packages offer the complementary-log-log link function, which is another cdf). I'm pretty sure your edited question is now a duplicate though.
Dec 8, 2015 at 17:40 comment added Sycorax Using the CDF of a normal curve is explicitly not logistic regression, as it does not use a logistic function. Models using the normal CDF are called probit. Yet another kind of -obit model is the robit, which uses the Cauchy CDF.
Dec 8, 2015 at 16:52 comment added Mitch I think what I'm trying to get at is why aren't other similarly shaped curves not measures of probability? Like $f(2x) = \frac{\tanh(x)+1}{2}$, or the CDF of the normal curve?
Dec 4, 2015 at 9:54 history answered Glen_b CC BY-SA 3.0