Definition: Unimodal and multimodal probability distribution

Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Probability distributions ▷ Unimodal vs. multimodal distribution

Definition: Let $X$ be a continuous random variable with some probability distribution $P$ characterized by probability density function $f_X(x)$. Then,

• $P$ is called a unimodal probability distribution, if $f_X(x)$ has exactly one maximum;

• $P$ is called a bimodal probability distribution, if $f_X(x)$ has exactly two maxima;

• $P$ is called a trimodal probability distribution, if $f_X(x)$ has exactly three maxima;

• $P$ is called a multimodal probability distribution, if $f_X(x)$ has more than one maximum.

Note that this definition of multimodality differs from the strict definition of the mode in which only the global maximum of $f_X(x)$ would be considered the single mode.

 

Sources:

• Weisstein, Eric W. (2024): "Mode"; in: Wolfram MathWorld, retrieved on 2024-10-25; URL: https://mathworld.wolfram.com/Mode.html.
• Wikipedia (2024): "Unimodality"; in: Wikipedia, the free encyclopedia, retrieved on 2024-10-25; URL: https://en.wikipedia.org/wiki/Unimodality#Unimodal_probability_distribution.

Metadata: ID: D207 | shortcut: dist-uni | author: JoramSoch | date: 2024-10-25, 12:04.