Inspired by reading this blog: https://garstats.wordpress.com/2017/11/28/trimmed-means/:
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Trimmed Mean
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| license: mit |
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| <!DOCTYPE html> | |
| <head> | |
| <meta charset="utf-8"> | |
| <link href="https://fonts.googleapis.com/css?family=Adamina" rel="stylesheet"> | |
| <script src="random.min.js"></script> | |
| <script src="prob.min.js"></script> | |
| <script src="https://d3js.org/d3.v4.min.js"></script> | |
| <style> | |
| body { | |
| font-family: 'Adamina', serif; | |
| margin: 50; | |
| } | |
| </style> | |
| </head> | |
| <body> | |
| <h1>Trimmed Mean</h1> | |
| <p>Inspired by reading this blog: <a href="https://garstats.wordpress.com/2017/11/28/trimmed-means/">https://garstats.wordpress.com/2017/11/28/trimmed-means/</a>:</p> | |
| <p><i>Trimmed means are robust estimators of central tendency. To compute a trimmed mean, we remove a predetermined amount of observations on each side of a distribution, and average the remaining observations.</i></p> | |
| <p>Choose the trim amount (from 0 to 0.45) to see the effect on the mean.</p> | |
| <div id="slidecontainer"> | |
| <p>Value: <span id="trim-value">0</span></p> | |
| </div> | |
| <script> | |
| const width = 1000 | |
| const height = 250 | |
| const margin = { "top": 20, "bottom": 20, "left": 20, "right": 20 } | |
| const data = [] | |
| let trimAmount = 0 | |
| let f = Prob.lognormal(1, 0.6); | |
| const dataLength = 1000 | |
| for (var i = 0; i < dataLength; i++) { | |
| data.push(Math.round(f())) | |
| }; | |
| data.sort(d3.ascending) | |
| const dataNested = d3.nest() | |
| .key(function (d) { return d }) | |
| .rollup(function (leaves) { return leaves.length; }) | |
| .entries(data) | |
| dataNested.forEach(function (d) { | |
| d.keyNumber = +d.key; | |
| }) | |
| let xScale = d3.scaleLinear() | |
| .range([0, width]) | |
| .domain([0, d3.max(dataNested, function (d) { return d.keyNumber })]) | |
| let yScale = d3.scaleLinear() | |
| .range([height, 0]) | |
| .domain([0, d3.max(dataNested, function (d) { return d.value })]) | |
| let area = d3.area() | |
| .x(function (d) { return xScale(d.keyNumber) }) | |
| .y0(function (d) { return yScale(0) }) | |
| .y1(function (d) { return yScale(d.value) }) | |
| .curve(d3.curveCatmullRom.alpha(0.5)); | |
| let line = d3.line() | |
| .x(function (d) { return xScale(d.keyNumber) }) | |
| .y(function (d) { return yScale(d.value) }) | |
| .curve(d3.curveCatmullRom.alpha(0.5)); | |
| let slider = d3.select("#slidecontainer").append("input") | |
| .attr("type", "range") | |
| .attr("min", 0) | |
| .attr("max", 0.4) | |
| .attr("value", 0) | |
| .attr("step", 0.05) | |
| .attr("id", "trim-slider") | |
| .on("input", function input() { | |
| update(); | |
| }); | |
| let svg = d3.select("body").append("svg") | |
| .attr("width", width + margin.left + margin.right) | |
| .attr("height", height + margin.top + margin.bottom) | |
| let g = svg.append("g") | |
| .attr("transform", "translate(" + margin.left + "," + margin.top + ")") | |
| g.append("g") | |
| .attr("transform", "translate(0," + height + ")") | |
| .call(d3.axisBottom(xScale)) | |
| g.append("g") | |
| .append("path") | |
| .datum(dataNested) | |
| .style("fill", "SandyBrown") | |
| .attr("d", area); | |
| g.append("g") | |
| .append("path") | |
| .datum(dataNested) | |
| .style("stroke", "#a7540c") | |
| .style("stroke-width", 3) | |
| .style("fill", "none") | |
| .attr("d", line) | |
| let trimRect = g.selectAll("rect") | |
| .data(trimExtent(data, trimAmount)) | |
| .enter() | |
| .append("rect") | |
| .attr("x", function (d) { | |
| return xScale(d.start) | |
| }) | |
| .attr("y", 0) | |
| .attr("width", function (d) { | |
| return xScale(d.end) - xScale(d.start) | |
| }) | |
| .attr("height", height) | |
| .style("fill", "grey") | |
| .style("opacity", 0.3) | |
| let avgLine = g.selectAll(".avg-line") | |
| .data([trimmedMean(data, trimAmount)]) | |
| .enter() | |
| .append("g") | |
| .attr("class", "avg-line") | |
| .attr("transform", function (d) { | |
| return "translate(" + xScale(d) + ",0)" | |
| }) | |
| avgLine.append("text") | |
| .text(function (d) { | |
| return "mean: " + round(d) | |
| }) | |
| .attr("x", 5) | |
| .attr("y", height * 0.9) | |
| avgLine.append("line") | |
| .attr("y2", height) | |
| .style("stroke", "black") | |
| .style("stroke-width", 3) | |
| .style("fill", "none") | |
| function trimmedMean(values, trim) { | |
| let l = values.length | |
| let n = Math.floor(l * trim) | |
| let trimmedValues = values.slice(n, l - n) | |
| let sum = trimmedValues.reduce((previous, current) => current += previous); | |
| return sum / (trimmedValues.length) | |
| } | |
| function trimExtent(values, trim) { | |
| let trimmedValues = values.sort(d3.ascending) | |
| let l = values.length | |
| let n = Math.floor(l * trim) | |
| return [{ "start": trimmedValues[n], "end": trimmedValues[l - n - 1] }] | |
| } | |
| function update() { | |
| var t = document.getElementById("trim-slider").value; | |
| d3.select("#trim-value").text(t) | |
| trimRect.data(trimExtent(data, t)) | |
| .transition() | |
| .attr("x", function (d) { | |
| return xScale(d.start) | |
| }) | |
| .attr("width", function (d) { | |
| return xScale(d.end) - xScale(d.start) | |
| }) | |
| let tm = trimmedMean(data, t) | |
| avgLine.data([tm]) | |
| .transition() | |
| .attr("transform", function (d) { | |
| return "translate(" + xScale(d) + ",0)" | |
| }) | |
| avgLine.select("text") | |
| .text("mean: " + round(tm)) | |
| } | |
| function round(n) { | |
| return Math.round(n * 100)/100 | |
| } | |
| </script> | |
| </body> |
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| /* Prob.js 1.0.6 (c) 2016 Google, Inc. License: Apache 2.0 */ | |
| !function(){"use strict";function assert(condition,message){if(!condition){if(message=message||"Assertion failed","undefined"!=typeof Error)throw new Error(message);throw message}}function binarySearch(arr,needle){for(var high=arr.length,low=-1;high-low>1;){var mid=Math.floor(low+(high-low)/2);arr[mid]<needle?low=mid:high=mid}return high}var root="object"==typeof self&&self.self===self&&self||"object"==typeof global&&global.global===global&&global||this,Prob={};"undefined"==typeof exports||exports.nodeType?root.Prob=Prob:("undefined"!=typeof module&&!module.nodeType&&module.exports&&(exports=module.exports=Prob),exports.Prob=Prob);var Random=root.Random||("function"==typeof require?require("random-js"):null);if(null===Random)throw"random-js is required https://github.com/ckknight/random-js";var mt=Random.engines.mt19937().autoSeed(),rand01=Random.real(0,1,!1),rand11=Random.real(-1,1,!0);Prob.Type={UNKNOWN:0,CONTINUOUS:1,DISCRETE:2},Prob.uniform=function(min,max){min="undefined"!=typeof min?min:0,max="undefined"!=typeof max?max:1;var range=max-min,f=function(rand){return min+rand01(rand||mt)*range};return f.Min=min,f.Max=max,f.Mean=min+range/2,f.Variance=(max-min)*(max-min)/12,f.Type=Prob.Type.CONTINUOUS,f},Prob.normal=function(mean,sd){mean="undefined"!=typeof mean?mean:0,sd="undefined"!=typeof sd?sd:1;var y1=null,y2=null,f=function(rand){if(null!==y2)return y1=y2,y2=null,y1*sd+mean;var x1,x2,w;do x1=rand11(rand||mt),x2=rand11(rand||mt),w=x1*x1+x2*x2;while(w>=1||0===w);return w=Math.sqrt(-2*Math.log(w)/w),y1=x1*w,y2=x2*w,y1*sd+mean};return f.Min=Number.NEGATIVE_INFINITY,f.Max=Number.POSITIVE_INFINITY,f.Mean=mean,f.Variance=sd*sd,f.Type=Prob.Type.CONTINUOUS,f},Prob.exponential=function(lambda){lambda="undefined"!=typeof lambda?lambda:1;var mean=1/lambda,f=function(rand){return-1*Math.log(rand01(rand||mt))*mean};return f.Min=0,f.Max=Number.POSITIVE_INFINITY,f.Mean=mean,f.Variance=Math.pow(lambda,-2),f.Type=Prob.Type.CONTINUOUS,f},Prob.lognormal=function(mu,sigma){mu="undefined"!=typeof mu?mu:0,sigma="undefined"!=typeof sigma?sigma:1;var nf=Prob.normal(mu,sigma),f=function(rand){return Math.exp(nf(rand))};return f.Min=0,f.Max=Number.POSITIVE_INFINITY,f.Mean=Math.exp(mu+sigma*sigma/2),f.Variance=(Math.exp(sigma*sigma)-1)*Math.exp(2*mu+sigma*sigma),f.Type=Prob.Type.CONTINUOUS,f},Prob.poisson=function(lambda){lambda="undefined"!=typeof lambda?lambda:1;var L=Math.exp(-lambda),f=function(rand){for(var k=0,p=1;;){if(p*=rand01(rand||mt),L>=p)break;k++}return k};return f.Min=0,f.Max=Number.POSITIVE_INFINITY,f.Mean=lambda,f.Variance=lambda,f.Type=Prob.Type.DISCRETE,f},Prob.zipf=function(s,N){s="undefined"!=typeof s?s:1,N="undefined"!=typeof N?N:100,assert(N>=1,"N must be >= 1");for(var sum=0,i=1;N>=i;i++)sum+=1/Math.pow(i,s);var cdf=[0],sumProb=0;for(i=1;N>=i;i++)sumProb+=1/(sum*Math.pow(i,s)),cdf[i]=sumProb;var f=function(rand){return binarySearch(cdf,rand01(rand||mt))};return f.Min=1,f.Max=N+1,f.Mean=null,f.Variance=null,f.Type=Prob.Type.DISCRETE,f},"function"==typeof define&&define.amd&&define("prob",[],function(){return Prob})}(); | |
| //# sourceMappingURL=prob-min.js.map |
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