Gallery: Add uniform distribution page

docs/examples/uniform_distribution.md

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+---
+jupytext:
+  text_representation:
+    extension: .md
+    format_name: myst
+kernelspec:
+  display_name: Python 3
+  language: python
+  name: python3
+---
+# Uniform Distribution
+
+The Uniform distribution is a continuous probability distribution bounded between two real numbers, $lower$ and $upper$, representing the lower and upper bounds, respectively.
+
+The probability density of the Uniform distribution is constant between $lower$ and $upper$ and zero elsewhere. Some experiments of physical origin exhibit this kind of behaviour. For instance, if we record, for a long time, the times at which radioactive particles are emitted within each hour, the outcomes will be uniform on the interval [0, 60] minutes interval.
+
+
+we encounter a continuous random variable that describes an experiment where the outcome is completely arbitrary, except that we know it lies between certain bounds. Many experiments of physical origin exhibit this kind of behavior. For instance, consider an experiment where we measure the emission of radioactive particles from some material over a long period. If we record the times at which particles are emitted within each hour, the outcomes will lie in the interval [0, 60] minutes
+
+The Uniform distribution is the maximum entropy probability distribution for a random variable under no constraint other than that it is contained in the interval $[lower,upper]$. It's often employed for generating random numbers from the cumulative distribution function (see [inverse transform sampling](https://en.wikipedia.org/wiki/Inverse_transform_sampling)). It is also used as the basis of some statistical tests (see [probability integral transform](https://en.wikipedia.org/wiki/Probability_integral_transform)). Sometimes, it can be used as a "non-informative" (flat) prior in Bayesian statistics when there is no prior knowledge about the parameter other than its range, but this is discouraged unless the range has a physical meaning and values outside of it are impossible. 
+
+## Probability Density Function (PDF):
+
+```{code-cell}
+---
+tags: [remove-input]
+mystnb:
+  image:
+    alt: Uniform Distribution PDF
+---
+
+import matplotlib.pyplot as plt
+import arviz as az
+from preliz import Uniform
+az.style.use('arviz-doc')
+ls = [1, -2]
+us = [6, 2]
+for l, u in zip(ls, us):
+    ax = Uniform(l, u).plot_pdf()
+ax.set_ylim(0, 0.3);
+
+```
+
+## Cumulative Distribution Function (CDF):
+
+```{code-cell}
+---
+tags: [remove-input]
+mystnb:
+  image:
+    alt: Uniform Distribution CDF
+---
+
+for l, u in zip(ls, us):
+    Uniform(l, u).plot_cdf()
+```
+
+## Key properties and parameters:
+
+```{eval-rst}
+========  =====================================
+Support   :math:`x \in [lower, upper]`
+Mean      :math:`\dfrac{lower + upper}{2}`
+Variance  :math:`\dfrac{(upper - lower)^2}{12}`
+========  =====================================
+```
+
+**Probability Density Function (PDF):**
+
+$$
+f(x \mid lower, upper) =
+    \begin{cases}
+        \dfrac{1}{upper - lower} & \text{for } x \in [lower, upper] \\
+        0 & \text{otherwise}
+    \end{cases}
+$$
+
+**Cumulative Distribution Function (CDF):**
+
+$$
+F(x \mid lower, upper) =
+    \begin{cases}
+        0 & \text{for } x < lower \\
+        \dfrac{x - lower}{upper - lower} & \text{for } x \in [lower, upper] \\
+        1 & \text{for } x > upper
+    \end{cases}
+$$
+
+```{seealso}
+:class: seealso
+
+
+
+**Related Distributions:**
+
+- [Beta Distribution](beta_distribution.md) - The Uniform distribution with $lower=0$, $upper=1$ is a special case of the Beta distribution with $\alpha = \beta = 1$.
+- [Beta Scaled Distribution](beta_scaled_distribution.md) - The Uniform distribution is a special case of the Beta Scaled distribution with $\alpha = \beta = 1$ and $lower$, $upper$ parameters.
+- [Discrete Uniform Distribution](discrete_uniform_distribution.md) - The discrete version of the Uniform distribution.
+```
+# References
+
+- Wikipedia - [Uniform distribution](https://en.wikipedia.org/wiki/Continuous_uniform_distribution)
+
+
+