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@jonsadka /.block
Last active May 29, 2017

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Binomial Probability Density
license: mit

binomial probability density function calculates success or failure. probability of x successes in n sucessive trials

Built with blockbuilder.org

<!DOCTYPE html>
<head>
<meta charset="utf-8">
<script src="https://d3js.org/d3.v4.min.js"></script>
<style>
body { margin:0;position:fixed;top:0;right:0;bottom:0;left:0; }
svg { width: 100%; height: 100%; }
</style>
</head>
<body>
<script>
var START_SUCCESS_RATE = 0.03;
var NUMBER_SUCCESS_RATE = 2;
var START_SAMPLE_SIZE = 30;
var NUMBER_SAMPLE_SIZE = 4;
var STEP_SAMPLE_SIZE = 10;
var NUMBER_HIRES = 3;
var margin = {top: 0, right: 0, bottom: 0, left: 0};
var width = 960 - margin.left - margin.right;
var height = 500 - margin.top - margin.bottom;
var svg = d3.select("body").append("svg")
.attr("width", width + margin.left + margin.right)
.attr("height", height + margin.top + margin.bottom)
.append("g")
.attr("transform", "translate(" + margin.left + "," + margin.top + ")")
.attr('id', 'transformGroup')
// calculates the probability that x or more out of a batch of n will be successful
// i.e. if 4% of candidates make it to hired, what is that chance that 4 out of 50 will get hired
// likelihood of hiring 10 candidates this month is 10% (we auto know what the batch size is because we know number in stage)
// if you move 30 more people to this stage, the likelihood increases to 20$
function calcChanceOfOccurence(pSuccessRate, nBatchSize, xFailureThreshold){
// throw new Error 'The success rate must be a percentage' if failureRate > 1
var qFailureRate = 1 - pSuccessRate;
var result = 1;
xFailureThreshold--;
while (xFailureThreshold >= 0){
// (n x) = n!/[(n-x)!x!]
var nOverX = factorial(nBatchSize)/( factorial(nBatchSize - xFailureThreshold) * factorial(xFailureThreshold) );
// p{3} = (n / x) * p^(x) * q^(n - x)
var p = nOverX * Math.pow(pSuccessRate, xFailureThreshold) * Math.pow(qFailureRate, (nBatchSize - xFailureThreshold));
result -= p;
xFailureThreshold--;
}
return result;
}
var f = [];
function factorial (n) {
if (n == 0 || n == 1)
return 1;
if (f[n] > 0)
return f[n];
return f[n] = factorial(n-1) * n;
}
const newData = d3.range(NUMBER_SUCCESS_RATE).map(idx => {
const chance = START_SUCCESS_RATE + 0.01*idx;
return d3.range(NUMBER_SAMPLE_SIZE).map(idx => (
{chance, n: START_SAMPLE_SIZE + STEP_SAMPLE_SIZE * idx, hire: NUMBER_HIRES}
));
});
const yScale = d3.scaleLinear()
.domain([0, 1])
.range([height, 0])
newData.forEach(data => {
const color = '#'+Math.floor(Math.random()*16777215).toString(16);
d3.select("#transformGroup").append('g')
.selectAll("circle").data(data).enter().append('circle')
.attr("cx", 0)
.attr("cy", d => yScale(calcChanceOfOccurence(d.chance, d.n, d.hire)))
.attr("r", 2)
.attr("fill", color)
.attr("opacity", 0.4)
.transition().duration(1000)
.attr("cx", d => calcChanceOfOccurence(d.chance, d.n, d.hire) * width)
.attr("r", 14)
d3.select("#transformGroup").append('g')
.selectAll("text").data(data).enter().append('text')
.text(d => Math.round(calcChanceOfOccurence(d.chance, d.n, d.hire)*1000)/10 + '% chance that ' + NUMBER_HIRES + ' hires will be made assuming '+ Math.round(d.chance*100) + '% success rate and ' + d.n + ' applicants')
.attr("cx", 0)
.attr("y", d => yScale(calcChanceOfOccurence(d.chance, d.n, d.hire)))
.attr("fill", color)
.attr("opacity", 0.8)
.transition().duration(1000)
.attr("x", d => 14 + calcChanceOfOccurence(d.chance, d.n, d.hire) * width)
})
</script>
</body>
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