src/centralF.html

<!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>