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liao961120 committed Mar 31, 2023
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7 changes: 7 additions & 0 deletions README.md
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Ordered Logit Interactive Visualization
=======================================

Play with it [here](https://yongfu.name/ordlogit).

Built upon a cool project: [probstats.org](https://github.com/probstats/probstats.github.io).

5 changes: 5 additions & 0 deletions build.sh
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monolith src/orderedLogit.html --no-fonts -o index.html
# After execution:
# 1. Remove `content="font-src 'none';"` in index.html
# 2. Copy & Paste KATEX/noUiSlider/d3 script tag from orderedLogit.html
# to index.html
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Large diffs are not rendered by default.

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MIT License

Copyright (c) 2021 Fred Feng

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
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## Interactive visualization of probability distributions

Tools used
- [D3.js](https://d3js.org/)
- [jStat](http://jstat.github.io/)
- [noUiSlider](https://refreshless.com/nouislider/)

We would like to thank [UM-Dearborn Open Educational Resources (OER)](https://guides.umd.umich.edu/OER_at_the_Mardigian_Library) for their support on this project.
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59 changes: 59 additions & 0 deletions src/bernoulli.html
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<!DOCTYPE html>
<html>
<meta charset="utf-8">

<head>
<title>Bernoulli distribution</title>
<meta name="viewport" content="width=device-width">
<link type="text/css" rel="stylesheet" media="screen" href="./css/page.css">
<link type="text/css" rel="stylesheet" media="screen" href="./css/chart.css">
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/noUiSlider/14.6.3/nouislider.min.css"/>
<script src="https://d3js.org/d3.v6.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/noUiSlider/14.6.3/nouislider.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/wnumb/1.2.0/wNumb.min.js"></script>
<script src="https://cdn.jsdelivr.net/npm/jstat@latest/dist/jstat.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS_HTML&delayStartupUntil=configured"></script>
<script src="./js/mathjax_config.js"></script>
</head>

<body>

<div class="container">

<h1>Bernoulli distribution</h1>

<p class="description">
Toss a coin, how likely it lands on heads (1) or tails (0)?
</p>

<div id="chart"></div>

<div class="controls">
<div class="slider-label">$p$</div>
<div id="slider_0"></div>
</div>

<div class="formula">
$$
p(k)=
\begin{cases}
p, & \text{if $k=1$,} \\
1-p, & \text{if $k=0$,} \\
0, & \text{otherwise.}
\end{cases}
\\[20pt]
\text{where $p$ is the probability the coin lands on heads.}
$$
</div>

</div>

</body>

<script src="./js/dist/bernoulli.js"></script>
<script src="./js/chart_config.js"></script>
<script src="./js/rand.js"></script>
<script src="./js/chart_function.js"></script>
<script src="./js/interact.js"></script>

</html>
54 changes: 54 additions & 0 deletions src/beta.html
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<!DOCTYPE html>
<html>
<meta charset="utf-8">

<head>
<title>Beta distribution</title>
<meta name="viewport" content="width=device-width">
<link type="text/css" rel="stylesheet" media="screen" href="./css/page.css">
<link type="text/css" rel="stylesheet" media="screen" href="./css/chart.css">
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/noUiSlider/14.6.3/nouislider.min.css"/>
<script src="https://d3js.org/d3.v6.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/noUiSlider/14.6.3/nouislider.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/wnumb/1.2.0/wNumb.min.js"></script>
<script src="https://cdn.jsdelivr.net/npm/jstat@latest/dist/jstat.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS_HTML&delayStartupUntil=configured"></script>
<script src="./js/mathjax_config.js"></script>
</head>

<body>

<div class="container">

<h1>Beta distribution</h1>

<div id="chart"></div>

<div class="controls">
<div class="slider-label">$\alpha$</div>
<div id="slider_0"></div>
</div>

<div class="controls">
<div class="slider-label">$\beta$</div>
<div id="slider_1"></div>
</div>

<div class="formula">
$$
f(x) = \frac{x^{\alpha-1}(1-x)^{\beta-1}}{\text{B}(\alpha, \beta)}
\\[20pt]
\text{where $\text{B}(\alpha, \beta)=\frac{\Gamma(\alpha)\Gamma(\beta)}{\Gamma(\alpha+\beta)}$ and $\Gamma$ is the Gamma function.} \\
$$
</div>
</div>

</body>

<script src="./js/dist/beta.js"></script>
<script src="./js/chart_config.js"></script>
<script src="./js/rand.js"></script>
<script src="./js/chart_function.js"></script>
<script src="./js/interact.js"></script>

</html>
64 changes: 64 additions & 0 deletions src/binomial.html
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<!DOCTYPE html>
<html>
<meta charset="utf-8">

<head>
<title>Binomial distribution</title>
<meta name="viewport" content="width=device-width">
<link type="text/css" rel="stylesheet" media="screen" href="./css/page.css">
<link type="text/css" rel="stylesheet" media="screen" href="./css/chart.css">
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/noUiSlider/14.6.3/nouislider.min.css"/>
<script src="https://d3js.org/d3.v6.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/noUiSlider/14.6.3/nouislider.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/wnumb/1.2.0/wNumb.min.js"></script>
<script src="https://cdn.jsdelivr.net/npm/jstat@latest/dist/jstat.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS_HTML&delayStartupUntil=configured"></script>
<script src="./js/mathjax_config.js"></script>
</head>

<body>

<div class="container">

<h1>Binomial distribution</h1>

<p class="description">
Tossing a coin $n$ times, how likely to get $k$ heads?
</p>

<div id="chart"></div>

<div class="controls">
<div class="slider-label">$n$</div>
<div id="slider_0"></div>
</div>

<div class="controls">
<div class="slider-label">$p$</div>
<div id="slider_1"></div>
</div>

<div class="formula">
$$
p(k) =
\begin{cases}
{n \choose k}p^k(1-p)^{n-k}, & \text{if $k = 0, 1, \cdots, n$,} \\
0, & \text{otherwise.}
\end{cases}
\\[16pt]
\text{where $p$ is the probability the coin lands on heads.}
$$
</div>

</div>

</body>

<script src="./js/dist/binomial.js"></script>
<script src="./js/chart_config.js"></script>
<script src="./js/rand.js"></script>
<script src="./js/chart_function.js"></script>
<script src="./js/interact.js"></script>


</html>
66 changes: 66 additions & 0 deletions src/centralF.html
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<!DOCTYPE html>
<html>
<meta charset="utf-8">

<head>
<title>F-distribution</title>
<meta name="viewport" content="width=device-width">
<link type="text/css" rel="stylesheet" media="screen" href="./css/page.css">
<link type="text/css" rel="stylesheet" media="screen" href="./css/chart.css">
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/noUiSlider/14.6.3/nouislider.min.css"/>
<script src="https://d3js.org/d3.v6.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/noUiSlider/14.6.3/nouislider.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/wnumb/1.2.0/wNumb.min.js"></script>
<script src="https://cdn.jsdelivr.net/npm/jstat@latest/dist/jstat.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS_HTML&delayStartupUntil=configured"></script>
<script src="./js/mathjax_config.js"></script>
</head>

<body>

<div class="container">

<h1>F-distribution</h1>

<p class="description">
The ratio of two (scaled) independent <a href="./chisquare.html">chi-square</a> random variables
</p>

<div id="chart"></div>

<div class="controls">
<div class="slider-label">$d_1$</div>
<div id="slider_0"></div>
</div>

<div class="controls">
<div class="slider-label">$d_2$</div>
<div id="slider_1"></div>
</div>

<div class="formula">
$$
X=\frac{\frac{1}{d_1}\sum_{i=1}^{d1} Z_i^2}{\frac{1}{d_2}\sum_{i=1}^{d2} Z_i^2}
$$
</div>

<div class="formula">
$$
f(x) = \frac{\sqrt{\frac{(d_1x)^{d_1}d_2^{d_2}}{(d_1x+d_2)^{d_1+d_2}}}}{x\text{B}\big(\frac{d_1}{2}, \frac{d_2}{2}\big)}
\\[24pt]
\text{where $d_1$ and $d_2$ are the degrees of freedom of the two} \\
\\
\text{chi-square random variables, and $\text{B}$ is the beta function.}
$$
</div>
</div>

</body>

<script src="./js/dist/centralF.js"></script>
<script src="./js/chart_config.js"></script>
<script src="./js/rand.js"></script>
<script src="./js/chart_function.js"></script>
<script src="./js/interact.js"></script>

</html>
65 changes: 65 additions & 0 deletions src/chisquare.html
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<!DOCTYPE html>
<html>
<meta charset="utf-8">

<head>
<title>Chi-square distribution</title>
<meta name="viewport" content="width=device-width">
<link type="text/css" rel="stylesheet" media="screen" href="./css/page.css">
<link type="text/css" rel="stylesheet" media="screen" href="./css/chart.css">
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/noUiSlider/14.6.3/nouislider.min.css"/>
<script src="https://d3js.org/d3.v6.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/noUiSlider/14.6.3/nouislider.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/wnumb/1.2.0/wNumb.min.js"></script>
<script src="https://cdn.jsdelivr.net/npm/jstat@latest/dist/jstat.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS_HTML&delayStartupUntil=configured"></script>
<script src="./js/mathjax_config.js"></script>
</head>

<body>

<div class="container">

<h1>Chi-square distribution</h1>

<p class="description">
A sum of the squares of $k$ independent <a href="./standardnormal.html">standard normal</a> random variables
</p>

<div id="chart"></div>

<div class="controls">
<div class="slider-label">$k$</div>
<div id="slider_0"></div>
</div>

<div class="formula">
$$
Z_1^2 + Z_2^2 + \cdots + Z_k^2 \;\sim\; \chi^2(k)
$$
</div>

<div class="formula">
$$
f(x) =
\begin{cases}
\frac{x^{\frac{k}{2}-1}e^{-\frac{x}{2}}}{2^{\frac{k}{2}}\Gamma\big(\frac{k}{2}\big)}, & \text{if $x > 0$,} \\
0, & \text{otherwise.}
\end{cases}
\\[24pt]
\text{where $k$ is the degree of freedom (the number of the squares)} \\
\\
\text{and $\Gamma\bigg(\frac{k}{2}\bigg)$ is the gamma function.}
$$
</div>
</div>

</body>

<script src="./js/dist/chisquare.js"></script>
<script src="./js/chart_config.js"></script>
<script src="./js/rand.js"></script>
<script src="./js/chart_function.js"></script>
<script src="./js/interact.js"></script>

</html>
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