added definition "dist-uni"

Author: JoramSoch

D/dist-uni.md

@@ -0,0 +1,46 @@
+---
+layout: definition
+mathjax: true
+
+author: "Joram Soch"
+affiliation: "BCCN Berlin"
+e_mail: "joram.soch@bccn-berlin.de"
+date: 2024-10-25 12:04:40
+
+title: "Unimodal and multimodal probability distribution"
+chapter: "General Theorems"
+section: "Probability theory"
+topic: "Probability distributions"
+definition: "Unimodal vs. multimodal"
+
+sources:
+  - authors: "Weisstein, Eric W."
+    year: 2024
+    title: "Mode"
+    in: "Wolfram MathWorld"
+    pages: "retrieved on 2024-10-25"
+    url: "https://mathworld.wolfram.com/Mode.html"
+  - authors: "Wikipedia"
+    year: 2024
+    title: "Unimodality"
+    in: "Wikipedia, the free encyclopedia"
+    pages: "retrieved on 2024-10-25"
+    url: "https://en.wikipedia.org/wiki/Unimodality#Unimodal_probability_distribution"
+
+def_id: "D207"
+shortcut: "dist-uni"
+username: "JoramSoch"
+---
+
+
+**Definition:** Let $X$ be a [continuous](/D/rvar-disc) [random variable](/D/rvar) with some [probability distribution](/D/dist) $P$ characterized by [probability density function](/P/pdf) $f_X(x)$. 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](/D/mode) in which only the global maximum of $f_X(x)$ [would be considered the single mode](/D/mode).