Distribution Gallery: Add Kumaraswamy (#548)

docs/examples/gallery/beta.md

@@ -152,7 +152,7 @@ where $B(x;\alpha,\beta)$ is the [Incomplete beta function](https://en.wikipedia
 
 **Common Alternatives:**
 
-- [Kumaraswamy](Kumaraswamy.md) -  It is similar to the Beta distribution, but with closed form expression for its probability density function, cumulative distribution function and quantile function.
+- [Kumaraswamy](kumaraswamy.md) -  It is similar to the Beta distribution, but with closed form expression for its probability density function, cumulative distribution function and quantile function.
 
 **Related Distributions:**
 - [Beta Scaled](beta_scaled.md) - A Beta distribution defined on an arbitrary range.

docs/examples/gallery/kumaraswamy.md

@@ -0,0 +1,91 @@
+---
+jupytext:
+  text_representation:
+    extension: .md
+    format_name: myst
+kernelspec:
+  display_name: Python 3
+  language: python
+  name: python3
+---
+# Kumaraswamy Distribution
+
+<audio controls> <source src="../../_static/kumaraswamy.mp3" type="audio/mpeg"> This browser cannot play the pronunciation audio file for this distribution. </audio>
+
+The Kumaraswamy distribution is a continuous probability distribution bounded between 0 and 1. It is characterized by two positive shape parameters: $a$ and $b$. 
+
+The Kumaraswamy distribution is a flexible distribution that can adopt a wide range of shapes, including uniform, U-shape, exponential-like, and many others, always restricted to the unit interval [0, 1].
+
+## Probability Density Function (PDF):
+
+```{code-cell}
+---
+tags: [remove-input]
+mystnb: image
+---
+import matplotlib.pyplot as plt
+
+from preliz import Kumaraswamy, style
+style.use('preliz-doc')
+
+a_s = [.5, 5., 1., 1., 2., 2.]
+b_s = [.5, 1., 1., 3., 2., 5.]
+
+for a, b in zip(a_s, b_s):
+    ax = Kumaraswamy(a, b).plot_pdf()
+    ax.set_ylim(0, 3.)
+```
+
+## Cumulative Distribution Function (CDF):
+
+```{code-cell}
+---
+tags: [remove-input]
+mystnb: image
+---
+for a, b in zip(a_s, b_s):
+    ax = Kumaraswamy(a, b).plot_cdf()
+```
+
+## Key properties and parameters:
+
+```{eval-rst}
+========  ==============================================================
+Support   :math:`x \in (0, 1)`
+Mean      :math:`b B(1 + \tfrac{1}{a}, b)`
+Variance  :math:`b B(1 + \tfrac{2}{a}, b) - (b B(1 + \tfrac{1}{a}, b))^2`
+========  ==============================================================
+```
+
+**Probability Density Function (PDF):**
+
+$$
+f(x|a, b) = a b x^{a-1} (1 - x^{a})^{b-1}
+$$
+
+
+**Cumulative Distribution Function (CDF):**
+
+$$
+F(x|a, b) = 1 - (1 - x^{a})^{b}
+$$
+
+
+```{seealso}
+:class: seealso
+
+**Common Alternatives:**
+
+- [Beta](beta.md) - The Kumaraswamy distribution is similar to the Beta distribution, but with closed-form expressions  for its probability density function, cumulative distribution function and quantile function.
+
+**Related Distributions:**
+
+- [Uniform](uniform.md) - The Uniform distribution on the interval [0, 1] is a special case of the Kumaraswamy distribution with $a = b = 1$.
+```
+
+## References
+
+- [Wikipedia - Kumaraswamy distribution](https://en.wikipedia.org/wiki/Kumaraswamy_distribution)
+
+
+

docs/gallery_content.rst

@@ -163,7 +163,7 @@ Continuous Distributions
       Inverse Gamma
 
    .. grid-item-card::
-      :link: ./api_reference.html#preliz.distributions.kumaraswamy.Kumaraswamy
+      :link: ./examples/gallery/kumaraswamy.html
       :text-align: center
       :shadow: none
       :class-card: example-gallery