3e:null 3f:["$","title",null,{"children":"Distribution shapes | Lincoln | Observable"}] 45:T400,dists = { return { raised_cosine: d3.ticks(-3, 3, 500).map((v) => { return { x: v, y: dist.raised_cosine(v, 0, 2.5) }; }), standard_normal: d3.ticks(-3, 3, 500).map((v) => { return { x: v, y: dist.dnorm(v, 0, 1) }; }), t_dist30: d3.ticks(-3, 3, 500).map((v) => { return { x: v, y: dist.dt(v, 30) }; }), t_dist20: d3.ticks(-3, 3, 500).map((v) => { return { x: v, y: dist.dt(v, 20) }; }), t_dist10: d3.ticks(-3, 3, 500).map((v) => { return { x: v, y: dist.dt(v, 10) }; }), t_dist7: d3.ticks(-3, 3, 500).map((v) => { return { x: v, y: dist.dt(v, 7) }; }), t_dist5: d3.ticks(-3, 3, 500).map((v) => { return { x: v, y: dist.dt(v, 5) }; }), uniform: d3.ticks(-2.1, 2.1, 500).map((v) => { return { x: v, y: dist.dunif(v, -2, 2) }; }) }; }46:[] 43:{"id":"7961f3272c5dfd3e","slug":"distribution-shapes","title":"Distribution shapes","thumbnail":"3dbf5c099d2c610cccb8c87c5dc19f81baffe9010fc9fab514bb37c1d08f967a","access_level":"public","create_time":"$D2022-08-29T13:23:39.737Z","update_time":"$D2022-09-03T12:19:31.045Z","view_time":null,"first_public_time":"$D2022-08-29T14:00:34.469Z","has_unpublished_edits":null,"fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"d0ef53fac0ab29d5","login":"ljcolling","name":"Lincoln","avatar_url":"https://avatars-next.observableusercontent.com/bdf2577c1c205964ad4657464c0fbaf1f1fe5b95b1440fefb07cf62cace3cc26","tier":"starter_2024","bio":"Cognitive scientist based at the University of Sussex"},"version":915,"publish_version":915,"role":null,"authored":false,"authors":[{"type":"individual","id":"0bcce7a4d3127de7","login":"ljcolling","name":"Lincoln","avatar_url":"https://avatars-next.observableusercontent.com/bdf2577c1c205964ad4657464c0fbaf1f1fe5b95b1440fefb07cf62cace3cc26","tier":null,"bio":"Cognitive scientist based at the University of Sussex"}],"members":[{"type":"individual","id":"0bcce7a4d3127de7","login":"ljcolling","name":"Lincoln","avatar_url":"https://avatars-next.observableusercontent.com/bdf2577c1c205964ad4657464c0fbaf1f1fe5b95b1440fefb07cf62cace3cc26","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Distribution shapes","cells":[{"id":0,"value":"# Distribution shapes","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":91,"value":"normal_plot_output = Plot.plot({\n x: {\n grid: true,\n domain: [-4, 4]\n },\n y: {\n grid: true,\n domain: [0, 0.8]\n },\n marks: [\n Plot.line(\n normal_plot(\n mean_value - sd_value * s > -4 ? mean_value - sd_value * s : -4,\n mean_value + sd_value * s < 4 ? mean_value + sd_value * s : 4,\n mean_value,\n sd_value\n ),\n {\n x: \"x\",\n y: \"y\",\n strokeWidth: 1,\n fill: \"blue\",\n opacity: show ? 0.5 : 0\n }\n ),\n Plot.line(fill_limits(s), {\n x: \"x\",\n y: \"y\",\n fill: \"blue\",\n strokeWidth: 1,\n opacity: show ? 0.5 : 0\n }),\n Plot.line(normal_plot(-4, 4, mean_value, sd_value), {\n x: \"x\",\n y: \"y\",\n strokeWidth: 4\n }),\n Plot.ruleY([0])\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":102,"value":"normal_sliders = htl.html`${mean_value_slider}${sd_value_slider}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":213,"value":"normal_description = texmd`This plot shows a normal distribution with a mean ($\\mu$) of ${mean_value} and a standard deviation ($\\sigma$) of ${sd_value}.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":762,"value":"viewof s = Inputs.range([0, 3], { step: 0.5 })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":816,"value":"viewof show = Inputs.toggle({ label: \"Show coverage\", value: false })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":850,"value":"md`The shaded area (± ${s} SDs from the mean) covers about ${coverage}% of the distribution.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":59,"value":"skew_normal_plot_output = Plot.plot({\n x: {\n grid: true\n },\n y: {\n grid: true,\n domain: [0, 0.8]\n },\n marks: [\n Plot.line(skew_normal_plot(-4, 4, skew), {\n x: \"x\",\n y: \"y\",\n strokeWidth: 4\n }),\n Plot.ruleY([0])\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":892,"value":"viewof skew = Inputs.range([-10, 10], { label: \"Skewness\", step: 0.5 })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":443,"value":"skew_adjust = htl.html`

${add_left}${add_right}

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":485,"value":"skew_desc = md`This distribution has a **skewness** of ${skew}. It is ${\n skew == 0 ? \"symmetrical\" : skew < 0 ? \"left-skewed\" : \"right-skewed\"\n}.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":238,"value":"kurtosis_plot = Plot.plot({\n x: {\n grid: true,\n domain: [-3, 3]\n },\n y: {\n grid: true,\n domain: [0, 0.4]\n },\n marks: [\n show_standard_normal\n ? Plot.line(dists.standard_normal, {\n x: \"x\",\n y: \"y\",\n stroke: \"grey\",\n strokeWidth: 1\n })\n : null,\n Plot.line(dists[Object.keys(kurtosis)[kurtosis_value]], {\n x: \"x\",\n y: \"y\",\n strokeWidth: 4\n }),\n Plot.ruleY([0])\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":901,"value":"viewof kurtosis_value = Inputs.range([0, 6], {\n step: 1,\n value: 2,\n label: \"Excess kurtosis\",\n format: (d) => kurtosis_values[d]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":567,"value":"htl.html`

${decrease_kurt}${increase_kurt}

`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":415,"value":"kurtosis_desc = md`This distribution has an excess kurtosis of ${\n kurtosis_values[kurtosis_value]\n}. ${\n kurtosis_values[kurtosis_value] === 0\n ? \"It is a **Mesokurtic distribution**.\"\n : kurtosis_values[kurtosis_value] > 0\n ? \"It is a **Leptokurtic distribution**.\"\n : \"It is a **Platykurtic distribution**.\"\n}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":623,"value":"\n\n\n\n\n### Dependencies","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":772,"value":"coverage = Math.round(\n 10000 *\n (dist.pnorm(sd_value * s + mean_value, mean_value, sd_value) -\n dist.pnorm(sd_value * -s + mean_value, mean_value, sd_value))\n) / 100","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":579,"value":"kurtosis_value_button = {\n const clamp = (num, min, max) => Math.min(Math.max(num, min), max);\n\n let dec = dec_kurt_value;\n let inc = add_kurt_value;\n let kurt_value = dec * -1 + inc;\n if (kurt_value == 0) {\n decrease_kurt[0].disabled = true;\n } else {\n decrease_kurt[0].disabled = false;\n }\n\n if (kurt_value == 6) {\n increase_kurt[0].disabled = true;\n } else {\n increase_kurt[0].disabled = false;\n }\n\n return kurt_value;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":433,"value":"skew_buttons = {\n let s = add_left_value * -1 + add_right_value * 1;\n if (s == -10) {\n add_left[0].disabled = true;\n } else {\n add_left[0].disabled = false;\n }\n\n if (s == 10) {\n add_right[0].disabled = true;\n } else {\n add_right[0].disabled = false;\n }\n return s;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":689,"value":"(decrease_kurt[0].disabled = true)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":675,"value":"clamp = (num, min, max) => Math.min(Math.max(num, min), max)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":581,"value":"dec_kurt_value = Generators.input(decrease_kurt)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":584,"value":" add_kurt_value = Generators.input(increase_kurt)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"// import jStat library\njStat = require(\"jStat\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":8,"value":"// jStat.normal.pdf( x, mean, std )\nnormal_plot = (min, max, mean, sd) => {\n // jStat.normal.pdf(x, mean, sd)\n\n return d3.ticks(min, max, 501).map((v) => {\n return {\n x: v,\n y: dist.dnorm(v, mean, sd)\n };\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":720,"value":"fill_limits = (mult) => {\n let s = sd_value * mult;\n return [\n { x: mean_value - s > -4 ? mean_value - s : -4, y: 0 },\n normal_plot(\n mean_value - s > -4 ? mean_value - s : -4,\n mean_value - s > -4 ? mean_value - s : -4,\n mean_value,\n sd_value\n )[0],\n normal_plot(\n mean_value + s < 4 ? mean_value + s : 4,\n mean_value + s < 4 ? mean_value + s : 4,\n mean_value,\n sd_value\n )[0],\n { x: mean_value + s < 4 ? mean_value + s : 4, y: 0 }\n ];\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":21,"value":"seq = (min, max, step) => d3.range(min, max, step).concat(max)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"d3.ticks(-6, 6, 101).map((v) => {\n return {\n x: v,\n y: jStat.normal.pdf(v, 0, 1)\n };\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":39,"value":"dsn = (x, alpha) => {\n // set the defaults\n\n const xi = 0;\n const omega = 1;\n const tau = 0;\n\n let z = (x - xi) / omega;\n\n let logN = -Math.log(Math.sqrt(2 * Math.PI)) - 0 - Math.pow(z, 2) / 2;\n\n let logS = Math.log(\n jStat.normal.cdf(tau * Math.sqrt(1 + Math.pow(alpha, 2)) + alpha * z, 0, 1)\n );\n\n let logPDF = logN + logS - Math.log(jStat.normal.cdf(tau, 0, 1));\n\n return Math.exp(logPDF);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":56,"value":"skew_normal_plot = (min, max, alpha) => {\n // jStat.normal.pdf(x, mean, sd)\n\n return d3.ticks(min, max, 201).map((v) => {\n return {\n x: v,\n y: dsn(v, alpha)\n };\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":429,"value":"add_left = Inputs.button(htl.html`

Left
Skew

`)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":431,"value":"add_right = Inputs.button(htl.html`Right
Skew`)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":453,"value":"add_left_value = Generators.input(add_left)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":464,"value":"add_right_value = Generators.input(add_right)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":99,"value":"mean_value_slider = Inputs.range([-3, 3], {\n value: 0,\n step: 0.25,\n label: htl.html`mean
μ`\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":105,"value":"sd_value_slider = Inputs.range([0.5, 2], {\n value: 1,\n step: 0.25,\n label: htl.html`standard deviation
σ`\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":161,"value":"sd_value = Generators.input(sd_value_slider)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":233,"value":"import { dist } from \"@ljcolling/wasm-distributions\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":214,"value":"import { texmd } from \"@kelleyvanevert/katex-within-markdown\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":164,"value":"normal_plot(-6, 6, 2, 1)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":569,"value":"decrease_kurt = Inputs.button(\n htl.html`

Decrease
Kurtosis

Increase
Kurtosis

`\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":115,"value":"mean_value = Generators.input(mean_value_slider)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":297,"value":"show_standard_normal = true","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":242,"value":"$45","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":313,"value":"kurtosis = {\n return {\n uniform: -(6 / 5),\n raised_cosine: (6 * (90 - Math.PI ** 4)) / (5 * (Math.PI ** 2 - 6) ** 2),\n standard_normal: 0,\n t_dist30: 6 / (30 - 4),\n t_dist20: 6 / (20 - 4),\n t_dist10: 6 / (10 - 4),\n t_dist7: 6 / (7 - 5),\n t_dist5: 6 / (5 - 4)\n };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":362,"value":"kurtosis_values = Object.values(kurtosis).map((v) => Math.round(v * 100) / 100)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W46","stdlib":"1"}} 44:"$43:body"