31:[] 2f:{"title":"Student-t fördelning (allmän version)","cells":[{"id":38,"value":"# Student-*t* fördelning (allmän version)","pinned":false,"hidden":false,"mode":"md"},{"id":406,"value":"### Modell","pinned":false,"hidden":false,"mode":"md"},{"id":408,"value":"moments = tex`\n\\begin{aligned}\n&X \\sim t_{\\nu}(\\mu,\\phi^2) \\\\[1em]\n&E( X) = \\mu \\text{ om }\\nu > 1 \\\\[1em]\n&Var( X) = \\frac{\\nu}{\\nu-2}\\phi^2\\text{ om } \\nu >2 \n\\end{aligned}\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":118,"value":"viewof myinputs = Inputs.form([\n Inputs.range([-5, 5], {value: 0, step: 0.1, label: tex`\\text{Läge }\\mu:`}),\n Inputs.range([0.1, 5], {value: 1, step: 0.1, label: tex`\\text{Skala }\\phi:`}),\n Inputs.range([1, 100], {value: 4, step: 1, label: tex`\\text{Frihetsgrader }\\nu:`}),\n Inputs.range([-10, 10], {value: -1.96, step: 0.01, label: \"Kvantil:\"})\n ])","pinned":false,"hidden":false,"mode":"ojs"},{"id":450,"value":"viewof shownormal = Inputs.toggle({value: false, label: \"visa normalfördelning\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":462,"value":"tailprobs = \n{\n var tailprobs;\n if (shownormal){\n tailprobs = tex`\\text{Normalfördelning: } P(X\\leq ${myinputs[3]})=${normcdf.toPrecision(4)} \\\\ \\text{Student-}t \\text{ fördelning: } P(X\\leq ${myinputs[3]})=${studentcdf.toPrecision(4)}`\n }\n else{\n tailprobs = tex`\\text{Student-}t \\text{ fördelning: } P(X\\leq ${myinputs[3]})=${studentcdf.toPrecision(4)}`\n }\n return tailprobs;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":305,"value":"plt = Plot.plot({\n color: {\n legend: shownormal\n },\n x: {\n label: \"x\",\n axis: true\n },\n y: {\n axis: false,\n domain: [0,1.05*jstat.normal.pdf(myinputs[0], myinputs[0], myinputs[1])]\n },\n marks: [\n Plot.ruleY([0]),\n Plot.line(data, {filter: d => d.dist == \"student-t\", x: \"x\", y: \"pdf\", stroke : \"dist\", strokeWidth: 2}),\n Plot.line(data, {filter: d => d.dist == \"normal\" && shownormal, x: \"x\", y: \"pdf\", stroke : \"dist\", strokeWidth: 2}),\n Plot.areaY(data, {filter: d => d.x <= myinputs[3] && d.dist == \"normal\" && shownormal, x: \"x\", y: \"pdf\", fill: \"steelblue\", opacity: 0.2}),\n Plot.areaY(data, {filter: d => d.x <= myinputs[3] && d.dist == \"student-t\", x: \"x\", y: \"pdf\", fill: \"orange\", opacity: 0.2}),\n \n ]\n })","pinned":false,"hidden":false,"mode":"ojs"},{"id":109,"value":"
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\n\n---\n## 🙈 Appendix 🙈\n\nHär följer bara kod och detaljer som du antagligen inte vill läsa.","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":223,"value":"#### Data","pinned":false,"hidden":false,"mode":"md"},{"id":17,"value":"data = {\n const x = d3.range(-10, 10, 0.01);\n const normpdf = x.map(x => ({x: x, pdf: jstat.normal.pdf(x, myinputs[0], myinputs[1]), dist: \"normal\"}));\n const studentpdf = x.map(x => ({x: x, pdf: jstat.studentt.pdf((x-myinputs[0])/myinputs[1], myinputs[2])/myinputs[1], dist: \"student-t\"}));\n const data = normpdf.concat(studentpdf)\n return data\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":19,"value":"normcdf = jstat.normal.cdf(myinputs[3], myinputs[0], myinputs[1]);","pinned":false,"hidden":false,"mode":"ojs"},{"id":23,"value":"studentcdf = jstat.studentt.cdf((myinputs[3]-myinputs[0])/myinputs[1], myinputs[2]);","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"}