2a:null 2b:["$","title",null,{"children":"Fisher Z-distribution | Mattias Villani | Observable"}] 31:T419,plt = { const p = Plot.plot({ style: { fontSize: "14px" }, color: { legend: true, domain: ["z", "normal (moment matched)"], range: [colors[2], colors[0]] }, x: { axis: null }, y: { axis: null, transform: (x) => { if (showlogpdf) { return Math.log(x) } else { return x } } }, marks: [ Plot.axisX({ label: null, fontSize: 12 }), Plot.axisY({ label: null, fontSize: 12 }), Plot.text(["x"], { frameAnchor: "bottom-right", fontSize: 16, dy: 30 }), Plot.text([yaxislabel], { frameAnchor: "left", fontSize: 16, rotate: -0, dy: -185, dx: -40 }), Plot.ruleY([0]), Plot.ruleX([-20]), Plot.line(data, { filter: d => d.dist == "z", x: "x", y: "pdf", stroke: colors[2], strokeWidth: 3 }), Plot.line(data, { filter: d => d.dist == "normal", x: "x", y: "pdf", stroke: colors[0], strokeWidth: 3 }), ] }) // directly set font size on all non-SVG text elements in the legend for (const el of p.querySelectorAll("span")) el.style.fontSize = "16px" return p }32:[] 2e:{"id":"17074c6ec5b85d54","slug":"zdist_simple","title":"Fisher Z-distribution","thumbnail":"6dfd0989a4e187ed74914b0756421f72589d20be91f0ced50ca7f61ec7141254","access_level":"public","create_time":"$D2026-05-28T09:16:40.911Z","update_time":"$D2026-05-28T20:16:40.266Z","view_time":null,"first_public_time":"$D2026-05-28T09:16:40.911Z","fork":{"id":"811384ce5401e838","slug":"z-distribution","title":"Fisher Z-distribution","owner":{"id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani"}},"stars":0,"starred":false,"owner":{"type":"team","id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":"pro_2024"},"version":1012,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"56499be8cf43f0ef","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":null}],"members":[{"type":"individual","id":"56499be8cf43f0ef","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":null,"role":"editor"},{"type":"team","id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":"pro_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":{"id":"738365a949244e81","slug":"talks","title":"Talks","owner":{"id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani"}},"type":"notebook","body":{"title":"Fisher Z-distribution","cells":[{"id":38,"value":"# Fisher *Z*-distribution","pinned":false,"hidden":false,"mode":"md"},{"id":722,"value":"html`

${tex`X \\sim \\mathcal{Z}(\\alpha, \\beta, \\mu, \\sigma) \\text{ for }X\\in\\mathbb{R}\\\\[1em]`}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":118,"value":"viewof myinputs = Inputs.form([\n Inputs.range([0.1, 3], {value: 0.5, step: 0.1, label: tex`\\alpha`}),\n Inputs.range([0.1, 3], {value: 0.5, step: 0.1, label: tex`\\beta`}),\n Inputs.range([-10, 10], {value: 0, step: 0.1, label: tex`\\mu`}),\n Inputs.range([0.1, 10], {value: 1, step: 0.01, label: tex`\\sigma`})\n ])","pinned":false,"hidden":false,"mode":"ojs"},{"id":450,"value":"viewof options = Inputs.form([\n Inputs.toggle({label: \"show pdf in logs\", value: false})\n ])","pinned":false,"hidden":false,"mode":"ojs"},{"id":305,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":109,"value":"
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\n\n---\n## 🙈 Appendix 🙈\n\nHere is only code and details that you probably don't want to read.","pinned":false,"hidden":false,"mode":"md"},{"id":221,"value":"#### Imports","pinned":false,"hidden":false,"mode":"md"},{"id":890,"value":"import {zpdf, zcdf, digamma, trigamma, colors} from \"@mattiasvillani/statistics-tools\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":26,"value":"jstat = require('jstat')","pinned":false,"hidden":false,"mode":"ojs"},{"id":223,"value":"#### Data","pinned":false,"hidden":false,"mode":"md"},{"id":874,"value":"yaxislabel = {if (showlogpdf){return \"log pdf\"}else{return \"pdf\"}}","pinned":true,"hidden":false,"mode":"ojs"},{"id":862,"value":"shownormal = true","pinned":false,"hidden":false,"mode":"ojs"},{"id":863,"value":"showlogpdf = options[0]","pinned":false,"hidden":false,"mode":"ojs"},{"id":511,"value":"alpha = myinputs[0]","pinned":false,"hidden":false,"mode":"ojs"},{"id":531,"value":"beta = myinputs[1]","pinned":false,"hidden":false,"mode":"ojs"},{"id":533,"value":"mu = myinputs[2]","pinned":false,"hidden":false,"mode":"ojs"},{"id":535,"value":"sigma = myinputs[3]","pinned":false,"hidden":false,"mode":"ojs"},{"id":819,"value":"quantile = myinputs[4]","pinned":false,"hidden":false,"mode":"ojs"},{"id":17,"value":"data = {\n const x = d3.range(-20, 20, 0.01);\n const normpdf = x.map(x => ({x: x, pdf: jstat.normal.pdf(x, Zmean, Zsd), dist: \"normal\"}));\n const zpdfval = x.map(x => ({x: x, pdf: zpdf(x, alpha, beta, mu, sigma), dist: \"z\"}));\n const data = normpdf.concat(zpdfval)\n return data\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":735,"value":"logdata = {\n const x = d3.range(-20, 20, 0.01);\n const normpdf = x.map(x => ({x: x, pdf: Math.log(jstat.normal.pdf(x, Zmean, Zsd)), dist: \"normal\"}));\n const zpdfval = x.map(x => ({x: x, pdf: zpdf(x, alpha, beta, mu, sigma, true), dist: \"z\"}));\n const data = normpdf.concat(zpdfval)\n return data\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":19,"value":"normcdf = jstat.normal.cdf(quantile, Zmean, Zsd);","pinned":false,"hidden":false,"mode":"ojs"},{"id":675,"value":"zcdfval = zcdf(quantile, alpha, beta, mu, sigma)","pinned":false,"hidden":false,"mode":"ojs"},{"id":834,"value":"datapdfmax = {\n const x = d3.range(0, 20, 0.01);\n const normpdf = x.map(x => ({x: x, pdf: normalpdfmax(x, Zmean, Zsd), dist: \"normal\"}));\n const zpdf = x.map(x => ({x: x, pdf: Zpdfmax(x, alpha, beta, mu, sigma), dist: \"z\"}));\n const data = normpdf.concat(zpdf)\n return data\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":839,"value":"function normalpdfmax(x, mu, sigma){\n return jstat.normal.pdf(x, mu, sigma)*jstat.normal.cdf(x, mu, sigma)**(n-1)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":542,"value":"#### Functions","pinned":false,"hidden":false,"mode":"md"},{"id":660,"value":"Zmean = mu + sigma*(digamma(alpha) - digamma(beta))","pinned":false,"hidden":false,"mode":"ojs"},{"id":670,"value":"Zsd = Math.sqrt(sigma**2*(trigamma(alpha) + trigamma(beta)))","pinned":false,"hidden":false,"mode":"ojs"},{"id":826,"value":"function Zpdfmax(x, alpha, beta, mu, sigma){\n return zpdf(x, alpha, beta, mu, sigma)*zcdf(x, alpha, beta, mu, sigma)**(n-1)\n}","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":"$W32","stdlib":"1","titling":"auto"}} 2f:"$2e:body"