Distribution Gallery: Add Categorical (#588)

* Distribution Gallery: Add Categorical

* Update docs/examples/gallery/categorical.md

---------

Co-authored-by: Osvaldo A Martin <aloctavodia@gmail.com>

docs/examples/gallery/categorical.md

@@ -0,0 +1,90 @@
+---
+jupytext:
+  text_representation:
+    extension: .md
+    format_name: myst
+kernelspec:
+  display_name: Python 3
+  language: python
+  name: python3
+---
+# Categorical Distribution
+
+<audio controls> <source src="../../_static/categorical.mp3" type="audio/mpeg"> This browser cannot play the pronunciation audio file for this distribution. </audio>
+
+The Categorical distribution is the most general discrete distribution and is parameterized by a vector $p$ where each element $p_i$ specifies the probabilities of each possible outcome.
+
+## Probability Density Function (PDF):
+
+```{code-cell}
+---
+tags: [remove-input]
+mystnb:
+  image:
+    alt: Categorical Distribution PDF
+---
+
+from preliz import Categorical, style
+style.use('preliz-doc')
+ps = [[0.1, 0.6, 0.3], [0.3, 0.1, 0.1, 0.5]]
+for p in ps:
+    Categorical(p).plot_pdf()
+```
+
+## Cumulative Distribution Function (CDF):
+
+```{code-cell}
+---
+tags: [remove-input]
+mystnb:
+  image:
+    alt: Categorical Distribution CDF
+---
+
+for p in ps:
+    Categorical(p).plot_cdf()
+```
+
+## Key properties and parameters:
+
+```{eval-rst}
+========  ===================================
+Support   :math:`x \in \{0, 1, \ldots, |p|-1\}`
+========  ===================================
+```
+
+**Probability Mass Function (PMF):**
+
+$$
+f(x) = p_x
+$$
+
+**Cumulative Distribution Function (CDF):**
+
+$$
+F(x \mid p) = \begin{cases}
+0 & \text{if } x < 0 \\
+\sum_{i=0}^{x} p_i & \text{if } 0 \leq x < |p| \\
+1 & \text{if } x \geq |p|
+\end{cases}
+$$
+
+where $p$ is the array of probabilities for each category.
+
+```{seealso}
+:class: seealso
+
+**Related Distributions:**
+
+- [Bernoulli](bernoulli.md) - The Categorical distribution is a generalization of the Bernoulli distribution to more than two outcomes.
+- [Discrete Uniform](discrete_uniform.md) - A special case of the Categorical distribution where all outcomes have equal probability.
+```
+
+## References
+
+- [Wikipedia - Categorical Distribution](https://en.wikipedia.org/wiki/Categorical_distribution)
+
+
+
+
+

docs/gallery_content.rst

@@ -432,7 +432,7 @@ Discrete Distributions
       Binomial
 
    .. grid-item-card::
-      :link: ./api_reference.html#preliz.distributions.categorical.Categorical
+      :link: ./examples/gallery/categorical.html
       :text-align: center
       :shadow: none
       :class-card: example-gallery