Demonstrating jenks natural breaks implemented in simple-statistics.
Rendered by d3js, based on an example by Mike Bostock.
Demonstrating jenks natural breaks implemented in simple-statistics.
Rendered by d3js, based on an example by Mike Bostock.
<!DOCTYPE html> | |
<meta charset="utf-8"> | |
<style> | |
body { | |
font:normal 14px sans-serif; | |
} | |
#form { | |
position: absolute; | |
top: 10px; | |
left: 10px; | |
} | |
input { | |
margin-right: 10px; | |
} | |
.states { | |
fill: none; | |
stroke: #fff; | |
stroke-linejoin: round; | |
} | |
path { | |
-webkit-transition: fill 200ms linear; | |
} | |
.q0-9 { fill:rgb(247,251,255); } | |
.q1-9 { fill:rgb(222,235,247); } | |
.q2-9 { fill:rgb(198,219,239); } | |
.q3-9 { fill:rgb(158,202,225); } | |
.q4-9 { fill:rgb(107,174,214); } | |
.q5-9 { fill:rgb(66,146,198); } | |
.q6-9 { fill:rgb(33,113,181); } | |
.q7-9 { fill:rgb(8,81,156); } | |
.q8-9 { fill:rgb(8,48,107); } | |
</style> | |
<body> | |
<div id='form'> | |
<input checked='true' type='radio' name='scale' id='jenks9' /><label for='jenks9'>jenks 9</label> | |
<input type='radio' name='scale' id='quantize' /><label for='quantize'>quantize</label> | |
</div> | |
<script src="http://d3js.org/d3.v3.min.js"></script> | |
<script src="simple_statistics.js"></script> | |
<script src="http://d3js.org/queue.v1.min.js"></script> | |
<script src="http://d3js.org/topojson.v0.min.js"></script> | |
<script> | |
var width = 960, | |
height = 500; | |
var scales = {}; | |
scales.quantize = d3.scale.quantize() | |
.domain([0, .15]) | |
.range(d3.range(9).map(function(i) { return "q" + i + "-9"; })); | |
var path = d3.geo.path(); | |
var svg = d3.select("body").append("svg") | |
.attr("width", width) | |
.attr("height", height); | |
queue() | |
.defer(d3.json, "/d/4090846/us.json") | |
.defer(d3.tsv, "unemployment.tsv") | |
.await(ready); | |
function ready(error, us, unemployment) { | |
var rateById = {}; | |
unemployment.forEach(function(d) { rateById[d.id] = +d.rate; }); | |
scales.jenks9 = d3.scale.threshold() | |
.domain(ss.jenks(unemployment.map(function(d) { return +d.rate; }), 9)) | |
.range(d3.range(9).map(function(i) { return "q" + i + "-9"; })); | |
var counties = svg.append("g") | |
.attr("class", "counties") | |
.selectAll("path") | |
.data(topojson.object(us, us.objects.counties).geometries) | |
.enter().append("path") | |
.attr("d", path); | |
d3.selectAll('input').on('change', function() { | |
setScale(this.id); | |
}); | |
function setScale(s) { | |
counties.attr("class", function(d) { return scales[s](rateById[d.id]); }) | |
} | |
setScale('jenks9'); | |
svg.append("path") | |
.datum(topojson.mesh(us, us.objects.states, function(a, b) { return a.id !== b.id; })) | |
.attr("class", "states") | |
.attr("d", path); | |
} | |
</script> |
// # simple-statistics | |
// | |
// A simple, literate statistics system. The code below uses the | |
// [Javascript module pattern](http://www.adequatelygood.com/2010/3/JavaScript-Module-Pattern-In-Depth), | |
// eventually assigning `simple-statistics` to `ss` in browsers or the | |
// `exports object for node.js | |
(function() { | |
var ss = {}; | |
if (typeof module !== 'undefined') { | |
// Assign the `ss` object to exports, so that you can require | |
// it in [node.js](http://nodejs.org/) | |
exports = module.exports = ss; | |
} else { | |
// Otherwise, in a browser, we assign `ss` to the window object, | |
// so you can simply refer to it as `ss`. | |
this.ss = ss; | |
} | |
// # [Linear Regression](http://en.wikipedia.org/wiki/Linear_regression) | |
// | |
// [Simple linear regression](http://en.wikipedia.org/wiki/Simple_linear_regression) | |
// is a simple way to find a fitted line | |
// between a set of coordinates. | |
ss.linear_regression = function() { | |
var linreg = {}, | |
data = []; | |
// Assign data to the model. Data is assumed to be an array. | |
linreg.data = function(x) { | |
if (!arguments.length) return data; | |
data = x.slice(); | |
return linreg; | |
}; | |
// ## Fitting The Regression Line | |
// | |
// This is called after `.data()` and returns the | |
// equation `y = f(x)` which gives the position | |
// of the regression line at each point in `x`. | |
linreg.line = function() { | |
//if there's only one point, arbitrarily choose a slope of 0 | |
//and a y-intercept of whatever the y of the initial point is | |
if (data.length == 1) { | |
m = 0; | |
b = data[0][1]; | |
} else { | |
// Initialize our sums and scope the `m` and `b` | |
// variables that define the line. | |
var sum_x = 0, sum_y = 0, | |
sum_xx = 0, sum_xy = 0, | |
m, b; | |
// Gather the sum of all x values, the sum of all | |
// y values, and the sum of x^2 and (x*y) for each | |
// value. | |
// | |
// In math notation, these would be SS_x, SS_y, SS_xx, and SS_xy | |
for (var i = 0; i < data.length; i++) { | |
sum_x += data[i][0]; | |
sum_y += data[i][1]; | |
sum_xx += data[i][0] * data[i][0]; | |
sum_xy += data[i][0] * data[i][1]; | |
} | |
// `m` is the slope of the regression line | |
m = ((data.length * sum_xy) - (sum_x * sum_y)) / | |
((data.length * sum_xx) - (sum_x * sum_x)); | |
// `b` is the y-intercept of the line. | |
b = (sum_y / data.length) - ((m * sum_x) / data.length); | |
} | |
// Return a function that computes a `y` value for each | |
// x value it is given, based on the values of `b` and `a` | |
// that we just computed. | |
return function(x) { | |
return b + (m * x); | |
}; | |
}; | |
return linreg; | |
}; | |
// # [R Squared](http://en.wikipedia.org/wiki/Coefficient_of_determination) | |
// | |
// The r-squared value of data compared with a function `f` | |
// is the sum of the squared differences between the prediction | |
// and the actual value. | |
ss.r_squared = function(data, f) { | |
if (data.length < 2) return 1; | |
// Compute the average y value for the actual | |
// data set in order to compute the | |
// _total sum of squares_ | |
var sum = 0, average; | |
for (var i = 0; i < data.length; i++) { | |
sum += data[i][1]; | |
} | |
average = sum / data.length; | |
// Compute the total sum of squares - the | |
// squared difference between each point | |
// and the average of all points. | |
var sum_of_squares = 0; | |
for (var j = 0; j < data.length; j++) { | |
sum_of_squares += Math.pow(average - data[j][1], 2); | |
} | |
// Finally estimate the error: the squared | |
// difference between the estimate and the actual data | |
// value at each point. | |
var err = 0; | |
for (var k = 0; k < data.length; k++) { | |
err += Math.pow(data[k][1] - f(data[k][0]), 2); | |
} | |
// As the error grows larger, it's ratio to the | |
// sum of squares increases and the r squared | |
// value grows lower. | |
return 1 - (err / sum_of_squares); | |
}; | |
// # [Bayesian Classifier](http://en.wikipedia.org/wiki/Naive_Bayes_classifier) | |
// | |
// This is a naïve bayesian classifier that takes | |
// singly-nested objects. | |
ss.bayesian = function() { | |
// The `bayes_model` object is what will be exposed | |
// by this closure, with all of its extended methods, and will | |
// have access to all scope variables, like `total_count`. | |
var bayes_model = {}, | |
// The number of items that are currently | |
// classified in the model | |
total_count = 0, | |
// Every item classified in the model | |
data = {}; | |
// ## Train | |
// Train the classifier with a new item, which has a single | |
// dimension of Javascript literal keys and values. | |
bayes_model.train = function(item, category) { | |
// If the data object doesn't have any values | |
// for this category, create a new object for it. | |
if (!data[category]) data[category] = {}; | |
// Iterate through each key in the item. | |
for (var k in item) { | |
var v = item[k]; | |
// Initialize the nested object `data[category][k][item[k]]` | |
// with an object of keys that equal 0. | |
if (data[category][k] === undefined) data[category][k] = {}; | |
if (data[category][k][v] === undefined) data[category][k][v] = 0; | |
// And increment the key for this key/value combination. | |
data[category][k][item[k]]++; | |
} | |
// Increment the number of items classified | |
total_count++; | |
}; | |
// ## Score | |
// Generate a score of how well this item matches all | |
// possible categories based on its attributes | |
bayes_model.score = function(item) { | |
// Initialize an empty array of odds per category. | |
var odds = {}, category; | |
// Iterate through each key in the item, | |
// then iterate through each category that has been used | |
// in previous calls to `.train()` | |
for (var k in item) { | |
var v = item[k]; | |
for (category in data) { | |
// Create an empty object for storing key - value combinations | |
// for this category. | |
if (odds[category] === undefined) odds[category] = {}; | |
// If this item doesn't even have a property, it counts for nothing, | |
// but if it does have the property that we're looking for from | |
// the item to categorize, it counts based on how popular it is | |
// versus the whole population. | |
if (data[category][k]) { | |
odds[category][k + '_' + v] = (data[category][k][v] || 0) / total_count; | |
} else { | |
odds[category][k + '_' + v] = 0; | |
} | |
} | |
} | |
// Set up a new object that will contain sums of these odds by category | |
var odds_sums = {}; | |
for (category in odds) { | |
// Tally all of the odds for each category-combination pair - | |
// the non-existence of a category does not add anything to the | |
// score. | |
for (var combination in odds[category]) { | |
if (odds_sums[category] === undefined) odds_sums[category] = 0; | |
odds_sums[category] += odds[category][combination]; | |
} | |
} | |
return odds_sums; | |
}; | |
// Return the completed model. | |
return bayes_model; | |
}; | |
// # sum | |
// | |
// is simply the result of adding all numbers | |
// together, starting from zero. | |
// | |
// This runs on `O(n)`, linear time in respect to the array | |
ss.sum = function(x) { | |
var sum = 0; | |
for (var i = 0; i < x.length; i++) { | |
sum += x[i]; | |
} | |
return sum; | |
}; | |
// # mean | |
// | |
// is the sum over the number of values | |
// | |
// This runs on `O(n)`, linear time in respect to the array | |
ss.mean = function(x) { | |
// The mean of no numbers is null | |
if (x.length === 0) return null; | |
return ss.sum(x) / x.length; | |
}; | |
// # geometric mean | |
// | |
// a mean function that is more useful for numbers in different | |
// ranges. | |
// | |
// this is the nth root of the input numbers multipled by each other | |
// | |
// This runs on `O(n)`, linear time in respect to the array | |
ss.geometric_mean = function(x) { | |
// The mean of no numbers is null | |
if (x.length === 0) return null; | |
// the starting value. | |
var value = 1; | |
for (var i = 0; i < x.length; i++) { | |
// the geometric mean is only valid for positive numbers | |
if (x[i] <= 0) return null; | |
// repeatedly multiply the value by each number | |
value *= x[i]; | |
} | |
return Math.pow(value, 1 / x.length); | |
}; | |
// Alias this into its common name | |
ss.average = ss.mean; | |
// # min | |
// | |
// This is simply the minimum number in the set. | |
// | |
// This runs on `O(n)`, linear time in respect to the array | |
ss.min = function(x) { | |
var min; | |
for (var i = 0; i < x.length; i++) { | |
// On the first iteration of this loop, min is | |
// undefined and is thus made the minimum element in the array | |
if (x[i] < min || min === undefined) min = x[i]; | |
} | |
return min; | |
}; | |
// # max | |
// | |
// This is simply the maximum number in the set. | |
// | |
// This runs on `O(n)`, linear time in respect to the array | |
ss.max = function(x) { | |
var max; | |
for (var i = 0; i < x.length; i++) { | |
// On the first iteration of this loop, min is | |
// undefined and is thus made the minimum element in the array | |
if (x[i] > max || max === undefined) max = x[i]; | |
} | |
return max; | |
}; | |
// # [variance](http://en.wikipedia.org/wiki/Variance) | |
// | |
// is the sum of squared deviations from the mean | |
ss.variance = function(x) { | |
// The variance of no numbers is null | |
if (x.length === 0) return null; | |
var mean = ss.mean(x), | |
deviations = []; | |
// Make a list of squared deviations from the mean. | |
for (var i = 0; i < x.length; i++) { | |
deviations.push(Math.pow(x[i] - mean, 2)); | |
} | |
// Find the mean value of that list | |
return ss.mean(deviations); | |
}; | |
// # [standard deviation](http://en.wikipedia.org/wiki/Standard_deviation) | |
// | |
// is just the square root of the variance. | |
ss.standard_deviation = function(x) { | |
// The standard deviation of no numbers is null | |
if (x.length === 0) return null; | |
return Math.sqrt(ss.variance(x)); | |
}; | |
ss.sum_squared_deviations = function(x) { | |
// The variance of no numbers is null | |
if (x.length <= 1) return null; | |
var mean = ss.mean(x), | |
sum = 0; | |
// Make a list of squared deviations from the mean. | |
for (var i = 0; i < x.length; i++) { | |
sum += Math.pow(x[i] - mean, 2); | |
} | |
return sum; | |
}; | |
// # [variance](http://en.wikipedia.org/wiki/Variance) | |
// | |
// is the sum of squared deviations from the mean | |
ss.sample_variance = function(x) { | |
var sum_squared_deviations = ss.sum_squared_deviations(x); | |
if (sum_squared_deviations === null) return null; | |
// Find the mean value of that list | |
return sum_squared_deviations / (x.length - 1); | |
}; | |
// # [standard deviation](http://en.wikipedia.org/wiki/Standard_deviation) | |
// | |
// is just the square root of the variance. | |
ss.sample_standard_deviation = function(x) { | |
// The standard deviation of no numbers is null | |
if (x.length <= 1) return null; | |
return Math.sqrt(ss.sample_variance(x)); | |
}; | |
// # [covariance](http://en.wikipedia.org/wiki/Covariance) | |
// | |
// sample covariance of two datasets: | |
// how much do the two datasets move together? | |
// x and y are two datasets, represented as arrays of numbers. | |
ss.sample_covariance = function(x, y) { | |
// The two datasets must have the same length which must be more than 1 | |
if (x.length <= 1 || x.length != y.length){ | |
return null; | |
} | |
// determine the mean of each dataset so that we can judge each | |
// value of the dataset fairly as the difference from the mean. this | |
// way, if one dataset is [1, 2, 3] and [2, 3, 4], their covariance | |
// does not suffer because of the difference in absolute values | |
var xmean = ss.mean(x), | |
ymean = ss.mean(y), | |
sum = 0; | |
// for each pair of values, the covariance increases when their | |
// difference from the mean is associated - if both are well above | |
// or if both are well below | |
// the mean, the covariance increases significantly. | |
for (var i = 0; i < x.length; i++){ | |
sum += (x[i] - xmean) * (y[i] - ymean); | |
} | |
// the covariance is weighted by the length of the datasets. | |
return sum / (x.length - 1); | |
}; | |
// # [correlation](http://en.wikipedia.org/wiki/Correlation_and_dependence) | |
// | |
// Gets a measure of how correlated two datasets are, between -1 and 1 | |
ss.sample_correlation = function(x, y) { | |
var cov = ss.sample_covariance(x, y), | |
xstd = ss.sample_standard_deviation(x), | |
ystd = ss.sample_standard_deviation(y); | |
if (cov === null || xstd === null || ystd === null) { | |
return null; | |
} | |
return cov / xstd / ystd; | |
}; | |
// # [median](http://en.wikipedia.org/wiki/Median) | |
ss.median = function(x) { | |
// The median of an empty list is null | |
if (x.length === 0) return null; | |
// Sorting the array makes it easy to find the center, but | |
// use `.slice()` to ensure the original array `x` is not modified | |
var sorted = x.slice().sort(function (a, b) { return a - b; }); | |
// If the length of the list is odd, it's the central number | |
if (sorted.length % 2 === 1) { | |
return sorted[(sorted.length - 1) / 2]; | |
// Otherwise, the median is the average of the two numbers | |
// at the center of the list | |
} else { | |
var a = sorted[(sorted.length / 2) - 1]; | |
var b = sorted[(sorted.length / 2)]; | |
return (a + b) / 2; | |
} | |
}; | |
// # [mode](http://bit.ly/W5K4Yt) | |
// This implementation is inspired by [science.js](https://github.com/jasondavies/science.js/blob/master/src/stats/mode.js) | |
ss.mode = function(x) { | |
// Handle edge cases: | |
// The median of an empty list is null | |
if (x.length === 0) return null; | |
else if (x.length === 1) return x[0]; | |
// Sorting the array lets us iterate through it below and be sure | |
// that every time we see a new number it's new and we'll never | |
// see the same number twice | |
var sorted = x.slice().sort(function (a, b) { return a - b; }); | |
// This assumes it is dealing with an array of size > 1, since size | |
// 0 and 1 are handled immediately. Hence it starts at index 1 in the | |
// array. | |
var last = sorted[0], | |
// store the mode as we find new modes | |
mode, | |
// store how many times we've seen the mode | |
max_seen = 0, | |
// how many times the current candidate for the mode | |
// has been seen | |
seen_this = 1; | |
// end at sorted.length + 1 to fix the case in which the mode is | |
// the highest number that occurs in the sequence. the last iteration | |
// compares sorted[i], which is undefined, to the highest number | |
// in the series | |
for (var i = 1; i < sorted.length + 1; i++) { | |
// we're seeing a new number pass by | |
if (sorted[i] !== last) { | |
// the last number is the new mode since we saw it more | |
// often than the old one | |
if (seen_this > max_seen) { | |
max_seen = seen_this; | |
seen_this = 1; | |
mode = last; | |
} | |
last = sorted[i]; | |
// if this isn't a new number, it's one more occurrence of | |
// the potential mode | |
} else { seen_this++; } | |
} | |
return mode; | |
}; | |
// # [t-test](http://en.wikipedia.org/wiki/Student's_t-test) | |
// | |
// This is to compute a one-sample t-test, comparing the mean | |
// of a sample to a known value, x. | |
// | |
// in this case, we're trying to determine whether the | |
// population mean is equal to the value that we know, which is `x` | |
// here. usually the results here are used to look up a | |
// [p-value](http://en.wikipedia.org/wiki/P-value), which, for | |
// a certain level of significance, will let you determine that the | |
// null hypothesis can or cannot be rejected. | |
ss.t_test = function(sample, x) { | |
// The mean of the sample | |
var sample_mean = ss.mean(sample); | |
// The standard deviation of the sample | |
var sd = ss.standard_deviation(sample); | |
// Square root the length of the sample | |
var rootN = Math.sqrt(sample.length); | |
// Compute the known value against the sample, | |
// returning the t value | |
return (sample_mean - x) / (sd / rootN); | |
}; | |
// # quantile | |
// This is a population quantile, since we assume to know the entire | |
// dataset in this library. Thus I'm trying to follow the | |
// [Quantiles of a Population](http://en.wikipedia.org/wiki/Quantile#Quantiles_of_a_population) | |
// algorithm from wikipedia. | |
// | |
// Sample is a one-dimensional array of numbers, | |
// and p is a decimal number from 0 to 1. In terms of a k/q | |
// quantile, p = k/q - it's just dealing with fractions or dealing | |
// with decimal values. | |
ss.quantile = function(sample, p) { | |
// We can't derive quantiles from an empty list | |
if (sample.length === 0) return null; | |
// invalid bounds. Microsoft Excel accepts 0 and 1, but | |
// we won't. | |
if (p >= 1 || p <= 0) return null; | |
// Sort a copy of the array. We'll need a sorted array to index | |
// the values in sorted order. | |
var sorted = sample.slice().sort(function (a, b) { return a - b; }); | |
// Find a potential index in the list. In Wikipedia's terms, this | |
// is I<sub>p</sub>. | |
var idx = (sorted.length) * p; | |
// If this isn't an integer, we'll round up to the next value in | |
// the list. | |
if (idx % 1 !== 0) { | |
return sorted[Math.ceil(idx) - 1]; | |
} else if (sample.length % 2 === 0) { | |
// If the list has even-length and we had an integer in the | |
// first place, we'll take the average of this number | |
// and the next value, if there is one | |
return (sorted[idx - 1] + sorted[idx]) / 2; | |
} else { | |
// Finally, in the simple case of an integer value | |
// with an odd-length list, return the sample value at the index. | |
return sorted[idx]; | |
} | |
}; | |
// Compute the matrices required for Jenks breaks. These matrices | |
// can be used for any classing of data with `classes <= n_classes` | |
ss.jenksMatrices = function(data, n_classes) { | |
// in the original implementation, these matrices are referred to | |
// as `LC` and `OP` | |
// | |
// * lower_class_limits (LC): optimal lower class limits | |
// * variance_combinations (OP): optimal variance combinations for all classes | |
var lower_class_limits = [], | |
variance_combinations = [], | |
// loop counters | |
i, j, | |
// the variance, as computed at each step in the calculation | |
variance = 0; | |
// Initialize and fill each matrix with zeroes | |
for (i = 0; i < data.length + 1; i++) { | |
var tmp1 = [], tmp2 = []; | |
for (j = 0; j < n_classes + 1; j++) { | |
tmp1.push(0); | |
tmp2.push(0); | |
} | |
lower_class_limits.push(tmp1); | |
variance_combinations.push(tmp2); | |
} | |
for (i = 1; i < n_classes + 1; i++) { | |
lower_class_limits[1][i] = 1; | |
variance_combinations[1][i] = 0; | |
// in the original implementation, 9999999 is used but | |
// since Javascript has `Infinity`, we use that. | |
for (j = 2; j < data.length + 1; j++) { | |
variance_combinations[j][i] = Infinity; | |
} | |
} | |
for (var l = 2; l < data.length + 1; l++) { | |
// `SZ` originally. this is the sum of the values seen thus | |
// far when calculating variance. | |
var sum = 0, | |
// `ZSQ` originally. the sum of squares of values seen | |
// thus far | |
sum_squares = 0, | |
// `WT` originally. This is the number of | |
w = 0, | |
// `IV` originally | |
i4 = 0; | |
// in several instances, you could say `Math.pow(x, 2)` | |
// instead of `x * x`, but this is slower in some browsers | |
// introduces an unnecessary concept. | |
for (var m = 1; m < l + 1; m++) { | |
// `III` originally | |
var lower_class_limit = l - m + 1, | |
val = data[lower_class_limit - 1]; | |
// here we're estimating variance for each potential classing | |
// of the data, for each potential number of classes. `w` | |
// is the number of data points considered so far. | |
w++; | |
// increase the current sum and sum-of-squares | |
sum += val; | |
sum_squares += val * val; | |
// the variance at this point in the sequence is the difference | |
// between the sum of squares and the total x 2, over the number | |
// of samples. | |
variance = sum_squares - (sum * sum) / w; | |
i4 = lower_class_limit - 1; | |
if (i4 !== 0) { | |
for (j = 2; j < n_classes + 1; j++) { | |
if (variance_combinations[l][j] >= | |
(variance + variance_combinations[i4][j - 1])) { | |
lower_class_limits[l][j] = lower_class_limit; | |
variance_combinations[l][j] = variance + | |
variance_combinations[i4][j - 1]; | |
} | |
} | |
} | |
} | |
lower_class_limits[l][1] = 1; | |
variance_combinations[l][1] = variance; | |
} | |
return { | |
lower_class_limits: lower_class_limits, | |
variance_combinations: variance_combinations | |
}; | |
}; | |
// # [Jenks natural breaks optimization](http://en.wikipedia.org/wiki/Jenks_natural_breaks_optimization) | |
// | |
// Implementations: [1](http://danieljlewis.org/files/2010/06/Jenks.pdf) (python), | |
// [2](https://github.com/vvoovv/djeo-jenks/blob/master/main.js) (buggy), | |
// [3](https://github.com/simogeo/geostats/blob/master/lib/geostats.js#L407) (works) | |
ss.jenks = function(data, n_classes) { | |
// sort data in numerical order | |
data = data.slice().sort(function (a, b) { return a - b; }); | |
// get our basic matrices | |
var matrices = ss.jenksMatrices(data, n_classes), | |
// we only need lower class limits here | |
lower_class_limits = matrices.lower_class_limits, | |
k = data.length - 1, | |
kclass = [], | |
countNum = n_classes; | |
// the calculation of classes will never include the upper and | |
// lower bounds, so we need to explicitly set them | |
kclass[n_classes] = data[data.length - 1]; | |
kclass[0] = data[0]; | |
// the lower_class_limits matrix is used as indexes into itself | |
// here: the `k` variable is reused in each iteration. | |
while (countNum > 1) { | |
kclass[countNum - 1] = data[lower_class_limits[k][countNum] - 2]; | |
k = lower_class_limits[k][countNum] - 1; | |
countNum--; | |
} | |
return kclass; | |
}; | |
// # Mixin | |
// | |
// Mixin simple_statistics to the Array native object. This is an optional | |
// feature that lets you treat simple_statistics as a native feature | |
// of Javascript. | |
ss.mixin = function() { | |
var support = !!(Object.defineProperty && Object.defineProperties); | |
if (!support) throw new Error('without defineProperty, simple-statistics cannot be mixed in'); | |
// only methods which work on basic arrays in a single step | |
// are supported | |
var arrayMethods = ['median', 'standard_deviation', 'sum', | |
'mean', 'min', 'max', 'quantile', 'geometric_mean']; | |
// create a closure with a method name so that a reference | |
// like `arrayMethods[i]` doesn't follow the loop increment | |
function wrap(method) { | |
return function() { | |
// cast any arguments into an array, since they're | |
// natively objects | |
var args = Array.prototype.slice.apply(arguments); | |
// make the first argument the array itself | |
args.unshift(this); | |
// return the result of the ss method | |
return ss[method].apply(ss, args); | |
}; | |
} | |
// for each array function, define a function off of the Array | |
// prototype which automatically gets the array as the first | |
// argument. We use [defineProperty](https://developer.mozilla.org/en-US/docs/JavaScript/Reference/Global_Objects/Object/defineProperty) | |
// because it allows these properties to be non-enumerable: | |
// `for (var in x)` loops will not run into problems with this | |
// implementation. | |
for (var i = 0; i < arrayMethods.length; i++) { | |
Object.defineProperty(Array.prototype, arrayMethods[i], { | |
value: wrap(arrayMethods[i]), | |
configurable: true, | |
enumerable: false, | |
writable: true | |
}); | |
} | |
}; | |
})(this); |
id | rate | |
---|---|---|
1001 | .097 | |
1003 | .091 | |
1005 | .134 | |
1007 | .121 | |
1009 | .099 | |
1011 | .164 | |
1013 | .167 | |
1015 | .108 | |
1017 | .186 | |
1019 | .118 | |
1021 | .099 | |
1023 | .127 | |
1025 | .17 | |
1027 | .159 | |
1029 | .104 | |
1031 | .085 | |
1033 | .114 | |
1035 | .195 | |
1037 | .14 | |
1039 | .101 | |
1041 | .097 | |
1043 | .096 | |
1045 | .093 | |
1047 | .211 | |
1049 | .143 | |
1051 | .09 | |
1053 | .129 | |
1055 | .107 | |
1057 | .128 | |
1059 | .123 | |
1061 | .1 | |
1063 | .147 | |
1065 | .127 | |
1067 | .099 | |
1069 | .089 | |
1071 | .118 | |
1073 | .107 | |
1075 | .148 | |
1077 | .105 | |
1079 | .136 | |
1081 | .086 | |
1083 | .093 | |
1085 | .185 | |
1087 | .114 | |
1089 | .075 | |
1091 | .148 | |
1093 | .152 | |
1095 | .092 | |
1097 | .111 | |
1099 | .187 | |
1101 | .102 | |
1103 | .104 | |
1105 | .198 | |
1107 | .13 | |
1109 | .087 | |
1111 | .151 | |
1113 | .126 | |
1115 | .107 | |
1117 | .076 | |
1119 | .139 | |
1121 | .136 | |
1123 | .137 | |
1125 | .09 | |
1127 | .119 | |
1129 | .151 | |
1131 | .256 | |
1133 | .175 | |
2013 | .101 | |
2016 | .084 | |
2020 | .07 | |
2050 | .148 | |
2060 | .036 | |
2068 | .034 | |
2070 | .084 | |
2090 | .069 | |
2100 | .062 | |
2110 | .057 | |
2122 | .097 | |
2130 | .061 | |
2150 | .066 | |
2164 | .059 | |
2170 | .088 | |
2180 | .121 | |
2185 | .057 | |
2188 | .132 | |
2201 | .136 | |
2220 | .059 | |
2232 | .073 | |
2240 | .081 | |
2261 | .064 | |
2270 | .204 | |
2280 | .098 | |
2282 | .063 | |
2290 | .136 | |
4001 | .148 | |
4003 | .074 | |
4005 | .077 | |
4007 | .109 | |
4009 | .144 | |
4011 | .215 | |
4012 | .089 | |
4013 | .085 | |
4015 | .102 | |
4017 | .142 | |
4019 | .084 | |
4021 | .118 | |
4023 | .172 | |
4025 | .095 | |
4027 | .242 | |
5001 | .143 | |
5003 | .091 | |
5005 | .082 | |
5007 | .053 | |
5009 | .064 | |
5011 | .078 | |
5013 | .062 | |
5015 | .043 | |
5017 | .096 | |
5019 | .063 | |
5021 | .104 | |
5023 | .059 | |
5025 | .06 | |
5027 | .081 | |
5029 | .065 | |
5031 | .059 | |
5033 | .066 | |
5035 | .099 | |
5037 | .071 | |
5039 | .076 | |
5041 | .099 | |
5043 | .091 | |
5045 | .06 | |
5047 | .059 | |
5049 | .061 | |
5051 | .066 | |
5053 | .057 | |
5055 | .082 | |
5057 | .086 | |
5059 | .073 | |
5061 | .072 | |
5063 | .078 | |
5065 | .077 | |
5067 | .092 | |
5069 | .092 | |
5071 | .061 | |
5073 | .086 | |
5075 | .079 | |
5077 | .082 | |
5079 | .082 | |
5081 | .056 | |
5083 | .077 | |
5085 | .052 | |
5087 | .053 | |
5089 | .112 | |
5091 | .045 | |
5093 | .113 | |
5095 | .074 | |
5097 | .058 | |
5099 | .087 | |
5101 | .062 | |
5103 | .071 | |
5105 | .056 | |
5107 | .088 | |
5109 | .063 | |
5111 | .075 | |
5113 | .064 | |
5115 | .062 | |
5117 | .067 | |
5119 | .06 | |
5121 | .073 | |
5123 | .094 | |
5125 | .058 | |
5127 | .063 | |
5129 | .059 | |
5131 | .062 | |
5133 | .051 | |
5135 | .078 | |
5137 | .066 | |
5139 | .095 | |
5141 | .091 | |
5143 | .05 | |
5145 | .067 | |
5147 | .091 | |
5149 | .064 | |
6001 | .113 | |
6003 | .152 | |
6005 | .121 | |
6007 | .122 | |
6009 | .143 | |
6011 | .145 | |
6013 | .112 | |
6015 | .119 | |
6017 | .112 | |
6019 | .141 | |
6021 | .138 | |
6023 | .103 | |
6025 | .301 | |
6027 | .095 | |
6029 | .139 | |
6031 | .139 | |
6033 | .147 | |
6035 | .118 | |
6037 | .127 | |
6039 | .123 | |
6041 | .08 | |
6043 | .088 | |
6045 | .101 | |
6047 | .157 | |
6049 | .111 | |
6051 | .103 | |
6053 | .1 | |
6055 | .087 | |
6057 | .109 | |
6059 | .094 | |
6061 | .113 | |
6063 | .139 | |
6065 | .147 | |
6067 | .122 | |
6069 | .125 | |
6071 | .136 | |
6073 | .102 | |
6075 | .097 | |
6077 | .155 | |
6079 | .09 | |
6081 | .09 | |
6083 | .085 | |
6085 | .118 | |
6087 | .102 | |
6089 | .147 | |
6091 | .137 | |
6093 | .135 | |
6095 | .115 | |
6097 | .099 | |
6099 | .153 | |
6101 | .151 | |
6103 | .137 | |
6105 | .159 | |
6107 | .149 | |
6109 | .127 | |
6111 | .11 | |
6113 | .109 | |
6115 | .178 | |
8001 | .081 | |
8003 | .055 | |
8005 | .069 | |
8007 | .062 | |
8009 | .034 | |
8011 | .05 | |
8013 | .055 | |
8014 | .066 | |
8015 | .051 | |
8017 | .02 | |
8019 | .07 | |
8021 | .051 | |
8023 | .084 | |
8025 | .076 | |
8027 | .052 | |
8029 | .066 | |
8031 | .077 | |
8033 | .132 | |
8035 | .059 | |
8037 | .062 | |
8039 | .06 | |
8041 | .072 | |
8043 | .077 | |
8045 | .058 | |
8047 | .06 | |
8049 | .058 | |
8051 | .044 | |
8053 | .022 | |
8055 | .072 | |
8057 | .033 | |
8059 | .067 | |
8061 | .028 | |
8063 | .029 | |
8065 | .071 | |
8067 | .047 | |
8069 | .056 | |
8071 | .07 | |
8073 | .037 | |
8075 | .046 | |
8077 | .082 | |
8079 | .053 | |
8081 | .056 | |
8083 | .063 | |
8085 | .069 | |
8087 | .049 | |
8089 | .058 | |
8091 | .041 | |
8093 | .061 | |
8095 | .026 | |
8097 | .05 | |
8099 | .05 | |
8101 | .075 | |
8103 | .039 | |
8105 | .048 | |
8107 | .06 | |
8109 | .078 | |
8111 | .053 | |
8113 | .042 | |
8115 | .033 | |
8117 | .058 | |
8119 | .067 | |
8121 | .032 | |
8123 | .075 | |
8125 | .026 | |
9001 | .078 | |
9003 | .088 | |
9005 | .079 | |
9007 | .067 | |
9009 | .089 | |
9011 | .076 | |
9013 | .067 | |
9015 | .09 | |
10001 | .079 | |
10003 | .086 | |
10005 | .073 | |
11001 | .117 | |
12001 | .071 | |
12003 | .114 | |
12005 | .089 | |
12007 | .083 | |
12009 | .111 | |
12011 | .098 | |
12013 | .082 | |
12015 | .127 | |
12017 | .121 | |
12019 | .098 | |
12021 | .131 | |
12023 | .09 | |
12027 | .117 | |
12029 | .123 | |
12031 | .112 | |
12033 | .098 | |
12035 | .162 | |
12037 | .071 | |
12039 | .096 | |
12041 | .1 | |
12043 | .1 | |
12045 | .098 | |
12047 | .113 | |
12049 | .126 | |
12051 | .168 | |
12053 | .138 | |
12055 | .116 | |
12057 | .115 | |
12059 | .072 | |
12061 | .152 | |
12063 | .072 | |
12065 | .085 | |
12067 | .072 | |
12069 | .123 | |
12071 | .139 | |
12073 | .072 | |
12075 | .121 | |
12077 | .053 | |
12079 | .117 | |
12081 | .127 | |
12083 | .133 | |
12085 | .119 | |
12086 | .113 | |
12087 | .07 | |
12089 | .107 | |
12091 | .072 | |
12093 | .133 | |
12095 | .114 | |
12097 | .128 | |
12099 | .117 | |
12101 | .125 | |
12103 | .112 | |
12105 | .127 | |
12107 | .122 | |
12109 | .09 | |
12111 | .153 | |
12113 | .094 | |
12115 | .123 | |
12117 | .106 | |
12119 | .09 | |
12121 | .098 | |
12123 | .104 | |
12125 | .084 | |
12127 | .117 | |
12129 | .072 | |
12131 | .068 | |
12133 | .096 | |
13001 | .097 | |
13003 | .126 | |
13005 | .085 | |
13007 | .091 | |
13009 | .116 | |
13011 | .067 | |
13013 | .111 | |
13015 | .133 | |
13017 | .153 | |
13019 | .124 | |
13021 | .1 | |
13023 | .097 | |
13025 | .116 | |
13027 | .087 | |
13029 | .081 | |
13031 | .09 | |
13033 | .122 | |
13035 | .127 | |
13037 | .111 | |
13039 | .091 | |
13043 | .093 | |
13045 | .108 | |
13047 | .08 | |
13049 | .106 | |
13051 | .085 | |
13053 | .146 | |
13055 | .114 | |
13057 | .095 | |
13059 | .07 | |
13061 | .082 | |
13063 | .123 | |
13065 | .11 | |
13067 | .096 | |
13069 | .168 | |
13071 | .09 | |
13073 | .07 | |
13075 | .119 | |
13077 | .1 | |
13079 | .095 | |
13081 | .121 | |
13083 | .09 | |
13085 | .101 | |
13087 | .127 | |
13089 | .107 | |
13091 | .112 | |
13093 | .101 | |
13095 | .111 | |
13097 | .114 | |
13099 | .105 | |
13101 | .067 | |
13103 | .079 | |
13105 | .122 | |
13107 | .103 | |
13109 | .089 | |
13111 | .1 | |
13113 | .084 | |
13115 | .111 | |
13117 | .086 | |
13119 | .118 | |
13121 | .107 | |
13123 | .098 | |
13125 | .111 | |
13127 | .082 | |
13129 | .131 | |
13131 | .098 | |
13133 | .111 | |
13135 | .094 | |
13137 | .094 | |
13139 | .091 | |
13141 | .177 | |
13143 | .113 | |
13145 | .072 | |
13147 | .138 | |
13149 | .124 | |
13151 | .104 | |
13153 | .073 | |
13155 | .145 | |
13157 | .109 | |
13159 | .127 | |
13161 | .135 | |
13163 | .149 | |
13165 | .196 | |
13167 | .119 | |
13169 | .086 | |
13171 | .153 | |
13173 | .084 | |
13175 | .108 | |
13177 | .079 | |
13179 | .085 | |
13181 | .103 | |
13183 | .059 | |
13185 | .082 | |
13187 | .111 | |
13189 | .121 | |
13191 | .096 | |
13193 | .13 | |
13195 | .083 | |
13197 | .099 | |
13199 | .132 | |
13201 | .087 | |
13205 | .104 | |
13207 | .102 | |
13209 | .085 | |
13211 | .098 | |
13213 | .123 | |
13215 | .092 | |
13217 | .126 | |
13219 | .062 | |
13221 | .082 | |
13223 | .107 | |
13225 | .102 | |
13227 | .108 | |
13229 | .093 | |
13231 | .118 | |
13233 | .108 | |
13235 | .071 | |
13237 | .104 | |
13239 | .118 | |
13241 | .104 | |
13243 | .13 | |
13245 | .103 | |
13247 | .12 | |
13249 | .138 | |
13251 | .137 | |
13253 | .107 | |
13255 | .154 | |
13257 | .107 | |
13259 | .107 | |
13261 | .129 | |
13263 | .098 | |
13265 | .124 | |
13267 | .087 | |
13269 | .13 | |
13271 | .162 | |
13273 | .116 | |
13275 | .093 | |
13277 | .106 | |
13279 | .098 | |
13281 | .078 | |
13283 | .119 | |
13285 | .129 | |
13287 | .13 | |
13289 | .114 | |
13291 | .09 | |
13293 | .133 | |
13295 | .096 | |
13297 | .11 | |
13299 | .107 | |
13301 | .188 | |
13303 | .14 | |
13305 | .117 | |
13307 | .091 | |
13309 | .091 | |
13311 | .095 | |
13313 | .125 | |
13315 | .116 | |
13317 | .117 | |
13319 | .107 | |
13321 | .108 | |
15001 | .108 | |
15003 | .063 | |
15007 | .096 | |
15009 | .097 | |
16001 | .091 | |
16003 | .121 | |
16005 | .084 | |
16007 | .052 | |
16009 | .121 | |
16011 | .059 | |
16013 | .077 | |
16015 | .071 | |
16017 | .095 | |
16019 | .059 | |
16021 | .12 | |
16023 | .045 | |
16025 | .11 | |
16027 | .106 | |
16029 | .06 | |
16031 | .059 | |
16033 | .041 | |
16035 | .118 | |
16037 | .039 | |
16039 | .077 | |
16041 | .04 | |
16043 | .066 | |
16045 | .104 | |
16047 | .055 | |
16049 | .083 | |
16051 | .068 | |
16053 | .059 | |
16055 | .087 | |
16057 | .059 | |
16059 | .065 | |
16061 | .052 | |
16063 | .097 | |
16065 | .055 | |
16067 | .06 | |
16069 | .055 | |
16071 | .05 | |
16073 | .041 | |
16075 | .077 | |
16077 | .067 | |
16079 | .119 | |
16081 | .051 | |
16083 | .068 | |
16085 | .114 | |
16087 | .084 | |
17001 | .079 | |
17003 | .112 | |
17005 | .093 | |
17007 | .138 | |
17009 | .045 | |
17011 | .109 | |
17013 | .095 | |
17015 | .105 | |
17017 | .073 | |
17019 | .082 | |
17021 | .099 | |
17023 | .131 | |
17025 | .114 | |
17027 | .079 | |
17029 | .091 | |
17031 | .106 | |
17033 | .105 | |
17035 | .097 | |
17037 | .092 | |
17039 | .092 | |
17041 | .091 | |
17043 | .086 | |
17045 | .107 | |
17047 | .091 | |
17049 | .079 | |
17051 | .116 | |
17053 | .104 | |
17055 | .146 | |
17057 | .125 | |
17059 | .11 | |
17061 | .092 | |
17063 | .114 | |
17065 | .093 | |
17067 | .113 | |
17069 | .128 | |
17071 | .094 | |
17073 | .086 | |
17075 | .1 | |
17077 | .073 | |
17079 | .095 | |
17081 | .1 | |
17083 | .088 | |
17085 | .081 | |
17087 | .104 | |
17089 | .099 | |
17091 | .128 | |
17093 | .104 | |
17095 | .103 | |
17097 | .1 | |
17099 | .124 | |
17101 | .103 | |
17103 | .109 | |
17105 | .107 | |
17107 | .095 | |
17109 | .077 | |
17111 | .093 | |
17113 | .074 | |
17115 | .124 | |
17117 | .105 | |
17119 | .097 | |
17121 | .119 | |
17123 | .106 | |
17125 | .143 | |
17127 | .08 | |
17129 | .078 | |
17131 | .089 | |
17133 | .078 | |
17135 | .122 | |
17137 | .084 | |
17139 | .09 | |
17141 | .119 | |
17143 | .116 | |
17145 | .119 | |
17147 | .082 | |
17149 | .081 | |
17151 | .106 | |
17153 | .119 | |
17155 | .15 | |
17157 | .094 | |
17159 | .105 | |
17161 | .095 | |
17163 | .108 | |
17165 | .112 | |
17167 | .079 | |
17169 | .066 | |
17171 | .075 | |
17173 | .1 | |
17175 | .098 | |
17177 | .116 | |
17179 | .113 | |
17181 | .108 | |
17183 | .12 | |
17185 | .103 | |
17187 | .08 | |
17189 | .08 | |
17191 | .097 | |
17193 | .086 | |
17195 | .106 | |
17197 | .099 | |
17199 | .096 | |
17201 | .155 | |
17203 | .086 | |
18001 | .134 | |
18003 | .093 | |
18005 | .088 | |
18007 | .09 | |
18009 | .133 | |
18011 | .068 | |
18013 | .078 | |
18015 | .099 | |
18017 | .105 | |
18019 | .082 | |
18021 | .096 | |
18023 | .092 | |
18025 | .105 | |
18027 | .049 | |
18029 | .089 | |
18031 | .11 | |
18033 | .124 | |
18035 | .095 | |
18037 | .08 | |
18039 | .15 | |
18041 | .134 | |
18043 | .074 | |
18045 | .116 | |
18047 | .089 | |
18049 | .112 | |
18051 | .067 | |
18053 | .111 | |
18055 | .071 | |
18057 | .061 | |
18059 | .078 | |
18061 | .078 | |
18063 | .068 | |
18065 | .12 | |
18067 | .119 | |
18069 | .111 | |
18071 | .101 | |
18073 | .087 | |
18075 | .104 | |
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