> For the complete documentation index, see [llms.txt](https://zavalab.gitbook.io/statschemebook/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://zavalab.gitbook.io/statschemebook/chapter-2-univariate-random-variables/01-models-of-univariate-rvs.md).

# Models of Univariate RVs

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**Slides:** [stats\_ch2\_univRV.pdf](https://github.com/vzavala/StatsBook/blob/master/Slides/stats_ch2_univRV.pdf) · [4-up handout](https://github.com/vzavala/StatsBook/blob/master/Slides/handouts/stats_ch2_univRV_4up.pdf) · **Code:** [Python notebooks](https://github.com/vzavala/StatsBook/tree/master/Python) · [MATLAB scripts](https://github.com/vzavala/StatsBook/tree/master/Matlab) · [MATLAB live scripts](https://github.com/vzavala/StatsBook/tree/master/Matlab-Live)
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* A wide range of RV models can be used to capture trends observed in real-life phenomena (e.g., diffusion, mixing, extreme events, particle sizes, failures).
* Type of model used depends on nature of phenomenon observed.
* Some of these models are “universal”, in the sense that they capture limiting behavior for many systems.
* We discuss properties of univariate RVs and connections between them.
* Many RVs result from algebraic transformations of other RVs (e.g., summations, logarithmic, exponential, quadratic).
* Later we explore estimation techniques to determine if an RV model matches data.
* Selection of an appropriate RV model is analogous to how we select a physical model that is appropriate for a specific application.