There are many different **bell shaped distributions** in statistics. The most well known is the “*bell curve*“, formally called the normal distribution. However, the normal distribution isn’t the only bell shaped distribution—there are others, including:

**Hyperbolic Secant Distribution**: symmetric member of the exponential family with a mean of 0 and variance of 1. It is similar to the normal distribution both in shape and symmetry but hyperbolic secant has slightly heavier tails [1].- The
**logistic distribution**also resembles a bell curve; it also has slightly heavier tails than the normal distribution. It appears in logistic regression and feedforward neural networks [2]. - The
**Cauchy distribution**is also bell shaped but the mean and variance are not defined. The median is given by a location parameter θ, and the spread is given by a scale parameter &simga;. The Cauchy distribution occurs as the ratio of two independent standard normal random variables [2]. - A
**Gaussian mixture model**is a probability distribution comprised of several weighted multivariate Gaussian (normal) distributions. The model is an overlapping of bell-shaped curves.

## Properties of a Bell Shaped Distribution

A bell shaped distribution is named because it looks like the shape of a bell when plotted on a graph. These distributions share several important properties:

- A single peak in the center (i.e., they are unimodal distributions).
- Symmetry: If you draw a vertical line down the center of the graph, the left half will mirror the right.

## References

PDF of the logistic distribution. Image: Krishnavedala| Wikimedia Commons

[1] M. J. Fischer, Generalized Hyperbolic Secant Distributions, 1

SpringerBriefs in Statistics, DOI: 10.1007/978-3-642-45138-6_1

[2] Ross, G. Probability/Density Distributions.

[3] Cunningham, A. Probability Playground: The Cauchy Distribution.