2e:null 2f:["$","title",null,{"children":"개미투자공학 번외편: Benford's Law와 재무제표의 부자연도 | Humble Data Miner | Observable"}] 34:T7bc,--- ## Benford's Law? * 현실세계의 수치데이터에서 **1SD**에 특정숫자가 나타날 확률은 다음과 같다 | 1SD | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | | **벤포드확률(%)** | 30.1% | 17.6% | 12.5% | 9.7% | 7.9% | 6.7% | 5.8% | 5.1% | 4.6% | * 확률표를 기준으로 설명하면 데이터(숫자의 집합)에서 아무숫자를 뽑았을때 * 그수의 **1SD**가 1일 확률은 30.1%이다, 9일 확률은 4.6%이다 * **Benford's Law**는 다양한 종류의 일반데이터에서 관찰된다 * 집값, 인구수, 주식가격, 요금고지서, 물리상수 등등 * 단, 숫자 단위가 제한적인경우 나타날경우 성립하지 않는다 * 키(대체로 160~200사이), 몸무게(대체로 45~110) 등등 * 확장된 형태로 **2SD**에 등장할 숫자의 확률 또한 계산할수 있다 | 2SD | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | | **벤포드확률(%)** | 12.0% | 11.4% | 10.9% | 10.4% | 10.0% | 9.7% | 9.3% | 9.0% | 8.8% | 8.5% | * **데이터의 확률**이 **벤포드확률**과 비슷할수록 자연스럽다 표현하면 * **데이터의 부자연도**는 다음과 같이 정의할수 있다([Cho 2007](https://www.tandfonline.com/doi/pdf/10.1198/000313007X223496?needAccess=true&role=button), [Morrow 2014](https://eprints.lse.ac.uk/60364/1/dp1291.pdf)) * **표본의 개수**를 ${tex`N`}, **데이터의 확률**을 ${tex`D_{Pr}`}, **벤포드확률**을 ${tex`B_{Pr}`}이라 하면 * ${tex`1SD 부자연도 = \sqrt{N}\sqrt{(D_{Pr}[1SD=1]-B_{Pr}[1SD=1])^2+(D_{Pr}[1SD=2]-B_{Pr}[1SD=2])^2+...+(D_{Pr}[1SD=9]-B_{Pr}[1SD=9])^2}`} * ${tex`2SD 부자연도 = \sqrt{N}\sqrt{(D_{Pr}[2SD=0]-B_{Pr}[2SD=0])^2+(D_{Pr}[2SD=1]-B_{Pr}[2SD=1])^2+...+(D_{Pr}[2SD=9]-B_{Pr}[2SD=9])^2}`} * 단순하게 설명하면, 확률값차이를 합산하고 표본수를 반영한것35:T11b9,bltest_population = { const data = worldpopulation2021; const rh = 1.0/data.length; const c1 = Array.from({length:10},_=>0); const c2 = Array.from({length:10},_=>0); const drawitems = []; for(let i=0; i < data.length; i++) { const numstr = data[i].pop.toString(); const x1 = parseInt(numstr[0]); const x2 = parseInt(numstr[1]); drawitems.push({x1:x1,x2:x2,y1:c1[x1]*rh,y2:c2[x2]*rh}); c1[x1]+=1; c2[x2]+=1; } const Dpr = {d1:c1.map(x=>x/data.length).slice(1),d2:c2.map(x=>x/data.length)}; console.log(Dpr); const dist = { d1:Math.sqrt(data.length*Bpr.d1.reduce((acc,cur,i)=>{acc += (cur-Dpr.d1[i])**2; return acc;},0)), d2:Math.sqrt(data.length*Bpr.d2.reduce((acc,cur,i)=>{acc += (cur-Dpr.d2[i])**2; return acc;},0)) }; const height = 400; const margin = {top: 50, right: 20, bottom: 30, left: 30}; const x1 = d3.scaleBand().domain(Array.from({length:9},(_,i)=>i+1)).range([margin.left, width/2]).paddingOuter(0.2).paddingInner(0.2); const x2 = d3.scaleBand().domain(Array.from({length:10},(_,i)=>i)).range([width/2+margin.left, width-margin.right]).paddingOuter(0.2).paddingInner(0.2); const y = d3.scaleLinear().domain([0,1]).range([height-margin.bottom,margin.top]); const svg = d3.create("svg").attr("viewBox", [0, 0, width, height]); const grect1 = svg.append("g").attr("fill","steelblue").attr("stroke","black").attr("stroke-opacity",0.2) .selectAll("rect") .data(drawitems) .join("rect") .attr("x",d=>x1(d.x1)).attr("y",d=>y(d.y1)).attr("width",x1.bandwidth()).attr("height",y(0)-y(rh)); const grect2 = svg.append("g").attr("fill","steelblue").attr("stroke","black").attr("stroke-opacity",0.2) .selectAll("rect") .data(drawitems) .join("rect") .attr("x",d=>x2(d.x2)).attr("y",d=>y(d.y2)).attr("width",x1.bandwidth()).attr("height",y(0)-y(rh)); const gBpr = svg.append("g"); gBpr.append("g") .selectAll("circle") .data(Bpr.d1) .join("circle") .attr("cx",(d,i)=>x1(i+1)+x1.bandwidth()/2).attr("cy",d=>y(d)) .attr("fill","black").attr("r",3).attr("stroke","white"); gBpr.append("g") .attr("dominant-baseline","auto").attr("text-anchor","middle") .attr("font-size","small").attr("style","text-shadow: 1px 1px 1px white") .selectAll("text") .data(Bpr.d1) .join("text") .attr("x",(d,i)=>x1(i+1)+x1.bandwidth()/2).attr("y",d=>y(d)).attr("dy",-5) .text(d=>d.toFixed(3)); gBpr.append("g") .selectAll("circle") .data(Bpr.d2) .join("circle") .attr("cx",(d,i)=>x2(i)+x2.bandwidth()/2).attr("cy",d=>y(d)) .attr("fill","black").attr("r",3).attr("stroke","white"); gBpr.append("g") .attr("dominant-baseline","auto").attr("text-anchor","middle") .attr("font-size","small").attr("style","text-shadow: 1px 1px 1px white") .selectAll("text") .data(Bpr.d2) .join("text") .attr("x",(d,i)=>x2(i)+x2.bandwidth()/2).attr("y",d=>y(d)).attr("dy",-5) .text(d=>d.toFixed(3)); const gdist = svg.append("g") gdist.append("text") .attr("dominant-baseline","hanging").attr("text-anchor","middle").attr("font-size", "larger") .attr("x", margin.left/2+width/4).attr("y", margin.top).text(`1SD부자연도=${dist.d1.toFixed(3)}`) gdist.append("text") .attr("dominant-baseline","hanging").attr("text-anchor","middle").attr("font-size", "larger") .attr("x", margin.left/2+width*3/4).attr("y", margin.top).text(`2SD부자연도=${dist.d2.toFixed(3)}`) svg.append("g").attr("transform",`translate(0,${height-margin.bottom})`).call(d3.axisBottom(x1)); svg.append("g").attr("transform",`translate(0,${height-margin.bottom})`).call(d3.axisBottom(x2)); svg.append("g").attr("transform",`translate(${margin.left},0)`).call(d3.axisLeft(y)); svg.append("g").attr("transform",`translate(${margin.left+width/2},0)`).call(d3.axisLeft(y)); const country = svg.append("text").attr("dominant-baseline","hanging").attr("text-anchor","middle"); const population = svg.append("text").attr("dominant-baseline","hanging").attr("text-anchor","middle"); return Object.assign(svg.node(), { update_country(ci) { country.attr("x",width/2).attr("y",0).text(data[ci].country); population.attr("x",width/2).attr("y",20).text(data[ci].pop.toLocaleString()); grect1.attr("visibility",(d,i)=>i<=ci?"visible":"hidden"); grect2.attr("visibility",(d,i)=>i<=ci?"visible":"hidden"); gdist.attr("opacity",ci/data.length); gBpr.attr("opacity",ci/data.length); } }); }36:T1ebe,krx_bltest_hexbin = { const height = 500; const data = krx_bltest_anonymized; const margin = {top: 20, right: 20, bottom: 70, left: 80}; const ex = [0,d3.max(data, d => d.D1)]; const ey = [0,d3.max(data, d => d.D2)]; const eratio = (ex[1]/ey[1]); const wide = (width/height) > eratio; const ps = wide?{width: height*eratio,height:height}:{width:width,height:width/eratio}; const radius = 5; const svg = d3.create("svg") .attr("viewBox", [0, 0, width, height]); const x = d3.scaleLinear().domain(ex).range([margin.left, ps.width - margin.right]); const y = d3.scaleLinear().domain(ey).range([ps.height - margin.bottom, margin.top]); const hexbin = d3.hexbin() .x(d => x(d.D1)) .y(d => y(d.D2)) .radius(radius * width / (height - 1)) .extent([[margin.left, margin.top], [ps.width - margin.right, ps.height - margin.bottom]]); const bins = hexbin(data); const color = d3.scaleSequential(d3.interpolateYlGnBu).domain([0, d3.max(bins, d => d.length)]); svg.append("g") .attr("stroke", "#000").attr("stroke-opacity", 0.1) .selectAll("path") .data(bins) .join("path") .attr("d", d => `M${d.x},${d.y}${hexbin.hexagon()}`) .attr("fill", d => color(d.length)); const triangle = d3.symbol(d3.symbolTriangle, 40); svg.append("g") .attr("stroke", "black").attr("stroke-width",0.4) .selectAll("path") .data(data.filter(d=>d.audit)) .join("path") .attr("transform",d=>`translate(${x(d.D1)},${y(d.D2)})`) .attr("fill", "orange") .attr("d",d=> triangle()); svg.append("g") .attr("stroke", "black").attr("stroke-width",0.4) .selectAll("path") .data(data.filter(d=>d.extaudit)) .join("path") .attr("transform",d=>`translate(${x(d.D1)},${y(d.D2)})`) .attr("fill", "red") .attr("d",d=> triangle()); svg.append("g") .selectAll("text") .data(data.filter(d=>d.stopped)) .join("text") .attr("dominant-baseline","middle").attr("text-anchor","middle") .attr("font-size", 10).attr("stroke", "darkred").attr("opacity", 0.8) .attr("x",d=>x(d.D1)).attr("y",d=>y(d.D2)) .text("🛇"); const cov = svg.append("g").append("path").attr("fill","steelblue").attr("stroke","none").attr("opacity",0.15); const lw = 230; const legend = svg.append("g").attr("transform",`translate(${ps.width-lw},${margin.top})`) .attr("dominant-baseline","middle").attr("text-anchor","start").attr("font-size","small"); legend.append("path").attr("transform",`translate(0,10)`).attr("fill", "orange").attr("d",triangle()); legend.append("text").attr("x",10).attr("y",10).text("조회공시(감사의견 비적정설)"); legend.append("path").attr("transform",`translate(0,30)`).attr("fill", "red").attr("d",triangle()); legend.append("text").attr("x",10).attr("y",30).text("조회공시(외부감사의견 비적정설)"); legend.append("text").attr("x",0).attr("y",50).attr("text-anchor","middle").attr("stroke","darkred").attr("fill","none").text("🛇"); legend.append("text").attr("x",10).attr("y",50).text("거래정지(비적정설로 인한)"); const medians = {d1:d3.median(data, d=>d.D1),d2:d3.median(data, d=>d.D2)}; svg.append("path").attr("d",`M ${x(medians.d1)} ${margin.top} V ${ps.height-margin.bottom}`) .attr("stroke","black").attr("stroke-dasharray","2 2").attr("opacity", 0.3); svg.append("text") .attr("dominant-baseline","middle").attr("text-anchor","middle") .attr("x",x(medians.d1)).attr("y",margin.top).text(`(중위 1SD부자연도)=${medians.d1.toFixed(3)}`); svg.append("path").attr("d",`M ${margin.left} ${y(medians.d2)} H ${ps.width-margin.right}`) .attr("stroke","black").attr("stroke-dasharray","2 2").attr("opacity", 0.3); svg.append("text") .attr("dominant-baseline","middle").attr("text-anchor","end") .attr("x",ps.width-margin.right).attr("y",y(medians.d2)).text(`(중위 2SD부자연도)=${medians.d2.toFixed(3)}`); svg.append("g").attr("transform", `translate(${ps.width-margin.right-200},0)`); svg.append("g").attr("transform",`translate(${margin.left},0)`).call(d3.axisLeft(y)); svg.append("g").attr("transform",`translate(0,${height-margin.bottom})`).call(d3.axisBottom(x)); const slider1 = d3_slider.sliderBottom() .min(d3.min(thresholds.d1)) .max(d3.max(thresholds.d1)) .marks(thresholds.d1) .width(x(d3.max(thresholds.d1))-x(d3.min(thresholds.d1))) .value(1.1) .tickFormat(x=>x.toFixed(2)) .fill("#eee") .on("onchange", () => _update_cov()); const thres_d1 = svg.append("g") .attr("class","thres_d1") .attr("transform",`translate(${x(d3.min(thresholds.d1))},${height-margin.bottom+30})`) .call(slider1); const slider2 = d3_slider.sliderLeft() .min(d3.min(thresholds.d2)) .max(d3.max(thresholds.d2)) .marks(thresholds.d2) .height(y(d3.min(thresholds.d2))-y(d3.max(thresholds.d2))) .value(1.1) .tickFormat(x=>x.toFixed(2)) .fill("#eee") .on("onchange", () => _update_cov()); const thres_d2 = svg.append("g") .attr("class","thres_d2") .attr("transform",`translate(${margin.left-30},${y(d3.max(thresholds.d2))})`) .call(slider2); thres_d1.selectAll("line.track-inset").attr("stroke","steelblue"); thres_d2.selectAll("line.track-inset").attr("stroke","steelblue"); const hs = Math.min(width-ps.width,400); const hm = 20; const heatmap = svg.append("g").attr("transform",`translate(${ps.width},${height-hs})`); const hx = d3.scaleBand().domain(thresholds.d1).range([hm,hs-2]).padding(0.01); heatmap.append("g").attr("transform",`translate(0,${hs-margin.bottom})`).call(d3.axisBottom(hx).tickFormat(d=>d.toFixed(2))); const hy = d3.scaleBand().domain(thresholds.d2).range([hs-margin.bottom,hm]).padding(0.01); heatmap.append("g").attr("transform",`translate(${hm},0)`).call(d3.axisLeft(hy).tickFormat(d=>d.toFixed(2))); const hrange = d3.extent(Object.values(scoretable),d=>d.fs); const hcolor = d3.scaleLinear().domain(hrange).range(["white",d3.color("darkgreen").darker()]) heatmap.append("g").selectAll("rect") .data(Object.values(scoretable)) .join("rect") .attr("x",d=>hx(d.t1)).attr("y",d=>hy(d.t2)).attr("width", hx.bandwidth()).attr("height", hy.bandwidth()).attr("fill", d => hcolor(d.fs)); heatmap.append("g").attr("dominant-baseline","middle").attr("text-anchor","middle").attr("font-size","small").selectAll("text") .data(Object.values(scoretable)) .join("text") .attr("x",d=>hx(d.t1)+hx.bandwidth()/2).attr("y",d=>hy(d.t2)+hy.bandwidth()/2) .attr("fill", "white").text(d=>(d.fs*100).toFixed(1)); const selected = heatmap.append("g").append("rect") .attr("width",hx.bandwidth()).attr("height",hy.bandwidth()).attr("fill","none").attr("stroke","red").attr("stroke-width",4); const measure = svg.append("g").attr("transform",`translate(${ps.width+hm},${margin.top})`) .attr("dominant-baseline","hanging").attr("text-anchor","start"); const precision = measure.append("text").attr("x",0).attr("y",0).attr("dy",4); const recall = measure.append("text").attr("x",0).attr("y",20).attr("dy",4); const fscore = measure.append("text").attr("x",0).attr("y",40).attr("dy",4); _update_cov(); function _update_cov() { update_cov(slider1.value(), slider2.value()); } function update_cov(d1,d2) { cov.attr("d", `M ${x(d1)} ${y(d2)} H ${margin.left} V ${margin.top} H ${ps.width-margin.right} V ${height-margin.bottom} H ${x(d1)} V ${y(d1)}`); selected.attr("x",hx(d1)).attr("y",hy(d2)); const score = scoretable[[d1,d2]]; precision.text(`Precision=${score.tp}/${score.tp+score.fp}=${score.pr.toFixed(4)}`); recall.text(`Recall=${score.tp}/${score.tp+score.fn}=${score.re.toFixed(2)}`); fscore.text(`F-score(β=10)*100=${(score.fs*100).toFixed(1)}`); } return svg.node(); 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32:{"id":"d3a8b203b1668939","slug":"benford-law-applied-to-krx-finance-reports","title":"개미투자공학 번외편: Benford's Law와 재무제표의 부자연도","thumbnail":"c9ac6ca24b31a8ec1ce8c7ff5387fca16deb8e3748fd3ac43c3c5729020009fb","access_level":"public","create_time":"$D2023-05-25T18:55:06.644Z","update_time":"$D2023-05-30T14:46:25.077Z","view_time":null,"first_public_time":"$D2023-05-25T18:55:06.644Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"50faa4da52a9ff9b","login":"humble-data-miner","name":"Humble Data Miner","avatar_url":"https://avatars-next.observableusercontent.com/3046b1bea86c5e825baea7c0c403d90ad9690b5396b11b5d02b3a0839fbcb946","tier":"starter_2024"},"version":787,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"4e2fc41e06361cc3","login":"humble-data-miner","name":"Humble Data 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Benford's Law와 재무제표의 부자연도","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":467,"value":"---\n## 용어 정리\n * 1SD(1st-Significant-Digit): 첫번째 자릿수, 예를들면 **3**1425의 **3**\n * 2SD(2nd-Significant-Digit): 두번째 자릿수, 예를들면 2**7**182의 **7**","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":200,"value":"$34","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":450,"value":"---\n## Benford's Law 적용예시(2021 국가별 인구수)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":393,"value":"viewof country_i = Scrubber(Array.from({length:worldpopulation2021.length},(_,i)=>i), {autoplay:false, loop:false, delay:100, format:(d,i)=>`(${i+1}/${worldpopulation2021.length}) ${worldpopulation2021[i].country}`});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":308,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":453,"value":"---\n## Benford's Law를 이용한 회계부정 탐지\n* 주요논리\n * 사람이 숫자를 조작할때, 부자연스럽게 숫자가 고루 나오도록 맞추는 경향\n * 데이터의 확률이 밴포드 확률에 근접하도록 인위적으로 맞추기 어려움\n* TV드라마/영화에서 연출된 Benford's Law를 이용한 회계부정 탐지\n\n|${await FileAttachment(\"Numb3rs_Poster@1.jpg\").image({style:\"width:200px\"})}| ${await FileAttachment(\"the accountant 2016@1.jpg\").image({style:\"width:200px\"})} | ${await FileAttachment(\"Ozark@1.png\").image({style:\"width:200px\"})} |\n| :-: | :-: | :-: |\n| Numb3rs Season 2 EP.15 \"The Running Man\" | 로봇공학회사의 횡령 탐지 | 카르텔 멤버의 재무제표에 숨겨진 금융사기 발견 |","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":500,"value":"---\n## Benford's Law를 KRX기업들의 재무제표에 적용하면?\n* (2016년 4분기 ~ 2022년 4분기) KRX 소속 기업들의 재무제표 14,646건\n * 사업보고서(4분기) 자료만 사용, 1분기/반기/3분기 보고서 제외\n * 각각 14,646건의 1SD부자연도와 2SD부자연도 계산\n* (2016년 4분기 ~ 2022년 4분기) 사이에 **감사의견 비적정설** 사례 94건 수집\n * 내부감사의견 비적정(81건) / 외부감사의견 비적정(13건) / 거래정지(16건)\n * 감사의견 비적정설 사례 데이터의 한계\n * 회계부정인지 아니면 정보미제공인지 등등 비적정설 원인 불명확\n * 전체 재무제표의 0.6%(94/14646)에 해당하는 극소량으로 대표성 부족\n * 대부분의 비적정 의견은 결산월의 사업보고서에 대해서만 존재","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":7,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":715,"value":"## 결과 해석 및 생각해볼만한 것들\n* 정성적 결과 해석\n * 부자연도를 이용한 비적정사례에 구별은 유의미\n * 전체분포에서 94건을 임의로 뽑는다면 빈도가 높은곳에 몰리겠지만\n * 비적정(94건)의 분포는 전체(14,646건)의 분포를 따르지 않음\n* 정량적 결과 해석\n * Precision: (비적정으로 옳게 판단된 건수) / (비적정으로 판단된 건수)\n * Recall: (비적정으로 옳게 판단된 건수) / (실제 비적정 건수)\n * F-score(β=10): Recall에 10배(β=10) 가중치를 두고 판단한 종합점수\n * 잘못 판단해 비적정을 놓치는 경우가 치명적, 따라서 Recall에 가중치\n * 1SD 부자연도 1.0 이상, 2SD 부자연도 1.1 이상일때 가장 높은 점수\n* 생각해볼만한것들\n * 중심점 기준으로 일정거리 이상의 사례들을 비적정 사례로 볼수있을까?\n * 중심점(1.1, 1.1)으로부터 비적정사례들이 주변으로 흩뿌려짐\n * 부자연도가 낮은 비적정사례는 숫자와 상관없는 비적정 사례들일까?\n * 부자연도가 높은 몇몇 비적정 사례들에 실제 숫자조작이 있었을까?\n\n## 마치며\n * 재무제표의 부자연도 활용방안\n * 기본적 분석으로 투자시 부자연도를 재무제표의 신뢰도 척도로 사용\n * 부자연도가 높은 몇몇 경우를 필터링해 고강도 회계감사\n * 개별회사의 회계감사는 정말로 성실히 수행되고 있을까?\n * 회계부정관련 연구자분들의 확장연구가 있었으면함","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":755,"value":"---\n## 참고 자료\n* [Benford's Law - Wikipedia](https://en.wikipedia.org/wiki/Benford%27s_law)\n* [전자공시시스템 | 공시서류검색 | 고급검색](https://dart.fss.or.kr/dsab009/main.do)\n* [Cho & Gaines (2007) Breaking the (Benford) Law, The American Statistician](https://www.tandfonline.com/doi/pdf/10.1198/000313007X223496?needAccess=true&role=button)\n* [Morrow (2014) Benford’s Law, Families of Distributions and a Test Basis](https://eprints.lse.ac.uk/60364/1/dp1291.pdf)\n* [World Population Prospects - UN Population Division](https://population.un.org/wpp/Download/Standard/MostUsed/)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":786,"value":"---\n## 부연설명 동영상\n\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":12,"value":"---\n## Appendix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":16,"value":"krx_bltest_anonymized = await FileAttachment(\"krx_bltest_anonymized.csv\").csv({typed: \"auto\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"krx_bltest_anonymized","database":"$undefined"},{"id":20,"value":"worldpopulation2021 = await FileAttachment(\"WorldPopulation2021@1.csv\").csv({typed: \"auto\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"worldpopulation2021","database":"$undefined"},{"id":360,"value":"Bpr = ({d1:[0.301,0.176,0.125,0.097,0.079,0.067,0.058,0.051,0.046],d2:[0.12,0.114,0.109,0.104,0.100,0.097,0.093,0.090, 0.088, 0.085]});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":555,"value":"thresholds = ({d1: d3.range(0.9, 1.45, 0.05), d2: d3.range(0.9, 1.45, 0.05)})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":588,"value":"scoretable = {\n const data = krx_bltest_anonymized;\n const beta = 10;\n const scoretable = {};\n for(const t1 of thresholds.d1) {\n for(const t2 of thresholds.d2) {\n const key = [t1,t2];\n const item = {\n t1: t1,\n t2: t2,\n tp:(data.filter(d=>(d.audit||d.extaudit||d.stopped)&&(d.D1>=t1||d.D2>=t2))).length,\n fp:(data.filter(d=>!(d.audit||d.extaudit||d.stopped)&&(d.D1>=t1||d.D2>=t2))).length,\n fn:(data.filter(d=>(d.audit||d.extaudit||d.stopped)&&!(d.D1>=t1||d.D2>=t2))).length,\n };\n item.pr = item.tp/(item.tp+item.fp);\n item.re = item.tp/(item.tp+item.fn);\n item.fs = (1+beta**2)*(item.pr*item.re)/((beta**2)*item.pr+item.re);\n scoretable[key]=item;\n }\n }\n return scoretable;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"d3 = require(\"d3\",\"d3-hexbin\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"html`\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":397,"value":"import {Scrubber} from \"@mbostock/scrubber\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":550,"value":"d3_slider= require(\"d3-simple-slider\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":410,"value":"bltest_population.update_country(country_i)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W37","stdlib":"1","titling":"auto"}} 33:"$32:body"