# What type of curve is this?

#### yccmp

##### New Member
The left one is a logistic curve / sigmoid function
e.g.
y=1 / 1+exp(-bx)

What would be the typical name for the curve on the right / typical functional form?

#### BGM

##### TS Contributor
The right one looks like a reflection of the left one along the diagonal line $$y = x$$

If this is true, then they are the inverse function of each other.

So for the right one, we have

$$x = \frac {1} {1 + e^{-\beta y}}$$

$$\Rightarrow 1 + e^{-\beta y} = \frac {1} {x}$$

$$\Rightarrow y = -\frac {1} {\beta} \ln\left(\frac {1} {x} - 1\right)$$

But you may have some further shifts on the curve depends on the location.