31:[] 2f:{"title":"Skew-normal distribution","cells":[{"id":38,"value":"# Skew-normal distribution","pinned":false,"hidden":false,"mode":"md"},{"id":629,"value":"

${tex`X\\sim \\mathrm{SkewN}(\\xi,\\omega,\\alpha)`}, for ${tex`-\\infty d.x <= quantile, x: \"x\", y: \"pdf\", fill: \"purple\", opacity: 0.2})\n ]\n })","pinned":false,"hidden":false,"mode":"ojs"},{"id":109,"value":"
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n\n---\n## 🙈 Appendix 🙈\n\nHere is some code and data details that you probably do not want to read.","pinned":false,"hidden":false,"mode":"md"},{"id":221,"value":"#### Imports","pinned":false,"hidden":false,"mode":"md"},{"id":26,"value":"jstat = require('jstat')","pinned":false,"hidden":false,"mode":"ojs"},{"id":750,"value":"mathjs = require('mathjs')","pinned":true,"hidden":false,"mode":"ojs"},{"id":223,"value":"#### Data","pinned":false,"hidden":false,"mode":"md"},{"id":654,"value":"xi = params[0]","pinned":false,"hidden":false,"mode":"ojs"},{"id":656,"value":"omega = params[1]","pinned":false,"hidden":false,"mode":"ojs"},{"id":802,"value":"alpha = params[2]","pinned":false,"hidden":false,"mode":"ojs"},{"id":662,"value":"quantile = params[3]","pinned":false,"hidden":false,"mode":"ojs"},{"id":806,"value":"delta = alpha/Math.sqrt((1+alpha**2))","pinned":false,"hidden":false,"mode":"ojs"},{"id":706,"value":"mean = xi + omega*delta*Math.sqrt(2/Math.PI)","pinned":false,"hidden":false,"mode":"ojs"},{"id":766,"value":"variance = omega**2 * (1 - (2*delta**2)/Math.PI) ","pinned":false,"hidden":false,"mode":"ojs"},{"id":813,"value":"skewness = ((4-Math.PI)/2) * (( delta*Math.sqrt(2/Math.PI) )**3 ) / ((1-(2*delta**2)/Math.PI)**(3/2))","pinned":false,"hidden":false,"mode":"ojs"},{"id":897,"value":"gridsize = 0.001","pinned":false,"hidden":false,"mode":"ojs"},{"id":830,"value":"function skewnormalpdf(x, xi, omega, alpha){\n const z = (x-xi)/omega\n return (2/omega)*jstat.normal.pdf(z,0,1)*jstat.normal.cdf(alpha*z,0,1)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":845,"value":"function skewnormalcdf(quantile,xi,omega,alpha,gridsize){\n return d3.sum(pdfdata.filter(d => d.x <=quantile).map(d => d.pdf)*gridsize)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":17,"value":"pdfdata = {\n const x = d3.range(-10, 10, gridsize); \n const pdf = x.map(x => ({x: x, pdf: skewnormalpdf(x, xi, omega, alpha )}));\n return pdf\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":19,"value":"cdf = d3.sum(pdfdata.filter(d => d.x <=quantile).map(d => d.pdf))*gridsize","pinned":false,"hidden":false,"mode":"ojs"},{"id":229,"value":"#### Style","pinned":false,"hidden":false,"mode":"md"},{"id":202,"value":"","pinned":false,"hidden":false,"mode":"html"},{"id":58,"value":"viewof md_colour = Inputs.color({label: \"Highlight color cells\", value: \"#F5F5DC\"})","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}