From the figure it can be seen that the sigmoid function becomes flat when its argument is highly positive or highly negative.

Graph of Sigmoid Function

The logistic sigmoid function can be used to define the $$\phi$$ parameter of a Bernoulli distribution because its output range is between 0 and 1. It is defined mathematically as $$\sigma(x) = \frac{1}{1+e^{-x}}$$.

San Jose State University

Google

There are some functions used while describing probability distribution in deep learning models they are
- Logistic Sigmoid
- Softplus Function


Properties of Common Functions

Goodfellow, I., Bengio, Y., & Courville, A. (2016). $\mathit{Deep \ Learning.}$ MIT Press. Retrieved from [www.deeplearningbook.org](https://www.deeplearningbook.org) 

Deep Learning

The softplus function can be used to define the $$\beta$$ or $$\sigma$$ parameter of a normal distribution because its output range is from 0 to $$\infty$$. It is defined mathematically as $$\zeta(x) = \log(1 + e^x)$$.

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