vega-statistics - npm Package Compare versions

Comparing version 1.5.0 to 1.6.0

build/vega-statistics.js

@@ -108,3 +108,67 @@ (function (global, factory) {
 
-  function quartiles(array, f) {
+  // Dot density binning for dot plot construction.
+  // Based on Leland Wilkinson, Dot Plots, The American Statistician, 1999.
+  // https://www.cs.uic.edu/~wilkinson/Publications/dotplots.pdf
+  function dotbin(array, step, smooth, f) {
+    f = f || (_ => _);
+
+    let i = 0, j = 1,
+        n = array.length,
+        v = new Float64Array(n),
+        a = f(array[0]),
+        b = a,
+        w = a + step,
+        x;
+
+    for (; j<n; ++j) {
+      x = f(array[j]);
+      if (x >= w) {
+        b = (a + b) / 2;
+        for (; i<j; ++i) v[i] = b;
+        w = x + step;
+        a = x;
+      }
+      b = x;
+    }
+
+    b = (a + b) / 2;
+    for (; i<j; ++i) v[i] = b;
+
+    return smooth ? smoothing(v, step + step / 4) : v;
+  }
+
+  // perform smoothing to reduce variance
+  // swap points between "adjacent" stacks
+  // Wilkinson defines adjacent as within step/4 units
+  function smoothing(v, thresh) {
+    let n = v.length,
+        a = 0,
+        b = 1,
+        c, d;
+
+    // get left stack
+    while (v[a] === v[b]) ++b;
+
+    while (b < n) {
+      // get right stack
+      c = b + 1;
+      while (v[b] === v[c]) ++c;
+
+      // are stacks adjacent?
+      // if so, compare sizes and swap as needed
+      if (v[b] - v[b-1] < thresh) {
+        d = b + ((a + c - b - b) >> 1);
+        while (d < b) v[d++] = v[b];
+        while (d > b) v[d--] = v[a];
+      }
+
+      // update left stack indices
+      a = b;
+      b = c;
+    }
+
+    return v;
+  }
+
+  function quantiles(array, p, f) {
     var values = Float64Array.from(numbers(array, f));
@@ -116,9 +180,9 @@
 
-    return [
-      d3Array.quantile(values, 0.25),
-      d3Array.quantile(values, 0.50),
-      d3Array.quantile(values, 0.75)
-    ];
+    return p.map(_ => d3Array.quantileSorted(values, _));
   }
 
+  function quartiles(array, f) {
+    return quantiles(array, [0.25, 0.50, 0.75], f);
+  }
+
   function lcg(seed) {
@@ -182,35 +246,16 @@ // Random numbers using a Linear Congruential Generator with seed value
 
-  function gaussian(mean, stdev) {
-    var mu,
-        sigma,
-        next = NaN,
-        dist = {};
+  const SQRT2PI = Math.sqrt(2 * Math.PI);
+  const SQRT2 = Math.SQRT2;
 
-    dist.mean = function(_) {
-      if (arguments.length) {
-        mu = _ || 0;
-        next = NaN;
-        return dist;
-      } else {
-        return mu;
-      }
-    };
+  let nextSample = NaN;
 
-    dist.stdev = function(_) {
-      if (arguments.length) {
-        sigma = _ == null ? 1 : _;
-        next = NaN;
-        return dist;
-      } else {
-        return sigma;
-      }
-    };
+  function sampleNormal(mean, stdev) {
+    mean = mean || 0;
+    stdev = stdev == null ? 1 : stdev;
 
-    dist.sample = function() {
-      var x = 0, y = 0, rds, c;
-      if (next === next) {
-        x = next;
-        next = NaN;
-        return x;
-      }
+    let x = 0, y = 0, rds, c;
+    if (nextSample === nextSample) {
+      x = nextSample;
+      nextSample = NaN;
+    } else {
       do {
@@ -222,60 +267,170 @@ x = exports.random() * 2 - 1;
       c = Math.sqrt(-2 * Math.log(rds) / rds); // Box-Muller transform
-      next = mu + y * c * sigma;
-      return mu + x * c * sigma;
-    };
+      x *= c;
+      nextSample = y * c;
+    }
+    return mean + x * stdev;
+  }
 
-    dist.pdf = function(x) {
-      var exp = Math.exp(Math.pow(x-mu, 2) / (-2 * Math.pow(sigma, 2)));
-      return (1 / (sigma * Math.sqrt(2*Math.PI))) * exp;
-    };
+  function densityNormal(value, mean, stdev) {
+    stdev = stdev == null ? 1 : stdev;
+    const z = (value - (mean || 0)) / stdev;
+    return Math.exp(-0.5 * z * z) / (stdev * SQRT2PI);
+  }
 
-    // Approximation from West (2009)
-    // Better Approximations to Cumulative Normal Functions
-    dist.cdf = function(x) {
-      var cd,
-          z = (x - mu) / sigma,
-          Z = Math.abs(z);
-      if (Z > 37) {
-        cd = 0;
+  // Approximation from West (2009)
+  // Better Approximations to Cumulative Normal Functions
+  function cumulativeNormal(value, mean, stdev) {
+    mean = mean || 0;
+    stdev = stdev == null ? 1 : stdev;
+
+    let cd,
+        z = (value - mean) / stdev,
+        Z = Math.abs(z);
+
+    if (Z > 37) {
+      cd = 0;
+    } else {
+      let sum, exp = Math.exp(-Z * Z / 2);
+      if (Z < 7.07106781186547) {
+        sum = 3.52624965998911e-02 * Z + 0.700383064443688;
+        sum = sum * Z + 6.37396220353165;
+        sum = sum * Z + 33.912866078383;
+        sum = sum * Z + 112.079291497871;
+        sum = sum * Z + 221.213596169931;
+        sum = sum * Z + 220.206867912376;
+        cd = exp * sum;
+        sum = 8.83883476483184e-02 * Z + 1.75566716318264;
+        sum = sum * Z + 16.064177579207;
+        sum = sum * Z + 86.7807322029461;
+        sum = sum * Z + 296.564248779674;
+        sum = sum * Z + 637.333633378831;
+        sum = sum * Z + 793.826512519948;
+        sum = sum * Z + 440.413735824752;
+        cd = cd / sum;
       } else {
-        var sum, exp = Math.exp(-Z*Z/2);
-        if (Z < 7.07106781186547) {
-          sum = 3.52624965998911e-02 * Z + 0.700383064443688;
-          sum = sum * Z + 6.37396220353165;
-          sum = sum * Z + 33.912866078383;
-          sum = sum * Z + 112.079291497871;
-          sum = sum * Z + 221.213596169931;
-          sum = sum * Z + 220.206867912376;
-          cd = exp * sum;
-          sum = 8.83883476483184e-02 * Z + 1.75566716318264;
-          sum = sum * Z + 16.064177579207;
-          sum = sum * Z + 86.7807322029461;
-          sum = sum * Z + 296.564248779674;
-          sum = sum * Z + 637.333633378831;
-          sum = sum * Z + 793.826512519948;
-          sum = sum * Z + 440.413735824752;
-          cd = cd / sum;
-        } else {
-          sum = Z + 0.65;
-          sum = Z + 4 / sum;
-          sum = Z + 3 / sum;
-          sum = Z + 2 / sum;
-          sum = Z + 1 / sum;
-          cd = exp / sum / 2.506628274631;
-        }
+        sum = Z + 0.65;
+        sum = Z + 4 / sum;
+        sum = Z + 3 / sum;
+        sum = Z + 2 / sum;
+        sum = Z + 1 / sum;
+        cd = exp / sum / 2.506628274631;
       }
-      return z > 0 ? 1 - cd : cd;
-    };
+    }
+    return z > 0 ? 1 - cd : cd;
+  }
 
-    // Approximation of Probit function using inverse error function.
-    dist.icdf = function(p) {
-      if (p <= 0 || p >= 1) return NaN;
-      var x = 2*p - 1,
-          v = (8 * (Math.PI - 3)) / (3 * Math.PI * (4-Math.PI)),
-          a = (2 / (Math.PI*v)) + (Math.log(1 - Math.pow(x,2)) / 2),
-          b = Math.log(1 - (x*x)) / v,
-          s = (x > 0 ? 1 : -1) * Math.sqrt(Math.sqrt((a*a) - b) - a);
-      return mu + sigma * Math.SQRT2 * s;
-    };
+  // Approximation of Probit function using inverse error function.
+  function quantileNormal(p, mean, stdev) {
+    if (p < 0 || p > 1) return NaN;
+    return (mean || 0) + (stdev == null ? 1 : stdev) * SQRT2 * erfinv(2 * p - 1);
+  }
 
+  // Approximate inverse error function. Implementation from "Approximating
+  // the erfinv function" by Mike Giles, GPU Computing Gems, volume 2, 2010.
+  // Ported from Apache Commons Math, http://www.apache.org/licenses/LICENSE-2.0
+  function erfinv(x) {
+    // beware that the logarithm argument must be
+    // commputed as (1.0 - x) * (1.0 + x),
+    // it must NOT be simplified as 1.0 - x * x as this
+    // would induce rounding errors near the boundaries +/-1
+    let w = - Math.log((1 - x) * (1 + x)), p;
+
+    if (w < 6.25) {
+        w -= 3.125;
+        p =  -3.6444120640178196996e-21;
+        p =   -1.685059138182016589e-19 + p * w;
+        p =   1.2858480715256400167e-18 + p * w;
+        p =    1.115787767802518096e-17 + p * w;
+        p =   -1.333171662854620906e-16 + p * w;
+        p =   2.0972767875968561637e-17 + p * w;
+        p =   6.6376381343583238325e-15 + p * w;
+        p =  -4.0545662729752068639e-14 + p * w;
+        p =  -8.1519341976054721522e-14 + p * w;
+        p =   2.6335093153082322977e-12 + p * w;
+        p =  -1.2975133253453532498e-11 + p * w;
+        p =  -5.4154120542946279317e-11 + p * w;
+        p =    1.051212273321532285e-09 + p * w;
+        p =  -4.1126339803469836976e-09 + p * w;
+        p =  -2.9070369957882005086e-08 + p * w;
+        p =   4.2347877827932403518e-07 + p * w;
+        p =  -1.3654692000834678645e-06 + p * w;
+        p =  -1.3882523362786468719e-05 + p * w;
+        p =    0.0001867342080340571352 + p * w;
+        p =  -0.00074070253416626697512 + p * w;
+        p =   -0.0060336708714301490533 + p * w;
+        p =      0.24015818242558961693 + p * w;
+        p =       1.6536545626831027356 + p * w;
+    } else if (w < 16.0) {
+        w = Math.sqrt(w) - 3.25;
+        p =   2.2137376921775787049e-09;
+        p =   9.0756561938885390979e-08 + p * w;
+        p =  -2.7517406297064545428e-07 + p * w;
+        p =   1.8239629214389227755e-08 + p * w;
+        p =   1.5027403968909827627e-06 + p * w;
+        p =   -4.013867526981545969e-06 + p * w;
+        p =   2.9234449089955446044e-06 + p * w;
+        p =   1.2475304481671778723e-05 + p * w;
+        p =  -4.7318229009055733981e-05 + p * w;
+        p =   6.8284851459573175448e-05 + p * w;
+        p =   2.4031110387097893999e-05 + p * w;
+        p =   -0.0003550375203628474796 + p * w;
+        p =   0.00095328937973738049703 + p * w;
+        p =   -0.0016882755560235047313 + p * w;
+        p =    0.0024914420961078508066 + p * w;
+        p =   -0.0037512085075692412107 + p * w;
+        p =     0.005370914553590063617 + p * w;
+        p =       1.0052589676941592334 + p * w;
+        p =       3.0838856104922207635 + p * w;
+    } else if (Number.isFinite(w)) {
+        w = Math.sqrt(w) - 5.0;
+        p =  -2.7109920616438573243e-11;
+        p =  -2.5556418169965252055e-10 + p * w;
+        p =   1.5076572693500548083e-09 + p * w;
+        p =  -3.7894654401267369937e-09 + p * w;
+        p =   7.6157012080783393804e-09 + p * w;
+        p =  -1.4960026627149240478e-08 + p * w;
+        p =   2.9147953450901080826e-08 + p * w;
+        p =  -6.7711997758452339498e-08 + p * w;
+        p =   2.2900482228026654717e-07 + p * w;
+        p =  -9.9298272942317002539e-07 + p * w;
+        p =   4.5260625972231537039e-06 + p * w;
+        p =  -1.9681778105531670567e-05 + p * w;
+        p =   7.5995277030017761139e-05 + p * w;
+        p =  -0.00021503011930044477347 + p * w;
+        p =  -0.00013871931833623122026 + p * w;
+        p =       1.0103004648645343977 + p * w;
+        p =       4.8499064014085844221 + p * w;
+    } else {
+        p = Infinity;
+    }
+
+    return p * x;
+  }
+
+  function gaussian(mean, stdev) {
+    var mu,
+        sigma,
+        dist = {
+          mean: function(_) {
+            if (arguments.length) {
+              mu = _ || 0;
+              return dist;
+            } else {
+              return mu;
+            }
+          },
+          stdev: function(_) {
+            if (arguments.length) {
+              sigma = _ == null ? 1 : _;
+              return dist;
+            } else {
+              return sigma;
+            }
+          },
+          sample: () => sampleNormal(mu, sigma),
+          pdf: value => densityNormal(value, mu, sigma),
+          cdf: value => cumulativeNormal(value, mu, sigma),
+          icdf: p => quantileNormal(p, mu, sigma)
+        };
+
     return dist.mean(mean).stdev(stdev);
@@ -341,2 +496,53 @@ }
 
+  function sampleLogNormal(mean, stdev) {
+    mean = mean || 0;
+    stdev = stdev == null ? 1 : stdev;
+    return Math.exp(mean + sampleNormal() * stdev);
+  }
+
+  function densityLogNormal(value, mean, stdev) {
+    if (value <= 0) return 0;
+    mean = mean || 0;
+    stdev = stdev == null ? 1 : stdev;
+    const z = (Math.log(value) - mean) / stdev;
+    return Math.exp(-0.5 * z * z) / (stdev * SQRT2PI * value);
+  }
+
+  function cumulativeLogNormal(value, mean, stdev) {
+    return cumulativeNormal(Math.log(value), mean, stdev);
+  }
+
+  function quantileLogNormal(p, mean, stdev) {
+    return Math.exp(quantileNormal(p, mean, stdev));
+  }
+
+  function lognormal(mean, stdev) {
+    var mu,
+        sigma,
+        dist = {
+          mean: function(_) {
+            if (arguments.length) {
+              mu = _ || 0;
+              return dist;
+            } else {
+              return mu;
+            }
+          },
+          stdev: function(_) {
+            if (arguments.length) {
+              sigma = _ == null ? 1 : _;
+              return dist;
+            } else {
+              return sigma;
+            }
+          },
+          sample: () => sampleLogNormal(mu, sigma),
+          pdf: value => densityLogNormal(value, mu, sigma),
+          cdf: value => cumulativeLogNormal(value, mu, sigma),
+          icdf: p => quantileLogNormal(p, mu, sigma)
+        };
+
+    return dist.mean(mean).stdev(stdev);
+  }
+
   function mixture(dists, weights) {
@@ -409,3 +615,3 @@ var dist = {}, m = 0, w;
 
-  function uniform(min, max) {
+  function sampleUniform(min, max) {
     if (max == null) {
@@ -415,42 +621,58 @@ max = (min == null ? 1 : min);
     }
+    return min + (max - min) * exports.random();
+  }
 
-    var dist = {},
-        a, b, d;
+  function densityUniform(value, min, max) {
+    if (max == null) {
+      max = (min == null ? 1 : min);
+      min = 0;
+    }
+    return (value >= min && value <= max) ? 1 / (max - min) : 0;
+  }
 
-    dist.min = function(_) {
-      if (arguments.length) {
-        a = _ || 0;
-        d = b - a;
-        return dist;
-      } else {
-        return a;
-      }
-    };
+  function cumulativeUniform(value, min, max) {
+    if (max == null) {
+      max = (min == null ? 1 : min);
+      min = 0;
+    }
+    return value < min ? 0 : value > max ? 1 : (value - min) / (max - min);
+  }
 
-    dist.max = function(_) {
-      if (arguments.length) {
-        b = _ || 0;
-        d = b - a;
-        return dist;
-      } else {
-        return b;
-      }
-    };
+  function quantileUniform(p, min, max) {
+    if (max == null) {
+      max = (min == null ? 1 : min);
+      min = 0;
+    }
+    return (p >= 0 && p <= 1) ? min + p * (max - min) : NaN;
+  }
 
-    dist.sample = function() {
-      return a + d * exports.random();
-    };
+  function uniform(min, max) {
+    var a, b,
+        dist = {
+          min: function(_) {
+            if (arguments.length) {
+              a = _ || 0;
+              return dist;
+            } else {
+              return a;
+            }
+          },
+          max: function(_) {
+            if (arguments.length) {
+              b = _ == null ? 1 : _;
+              return dist;
+            } else {
+              return b;
+            }
+          },
+          sample: () => sampleUniform(a, b),
+          pdf: value => densityUniform(value, a, b),
+          cdf: value => cumulativeUniform(value, a, b),
+          icdf: p => quantileUniform(p, a, b)
+        };
 
-    dist.pdf = function(x) {
-      return (x >= a && x <= b) ? 1 / d : 0;
-    };
-
-    dist.cdf = function(x) {
-      return x < a ? 0 : x > b ? 1 : (x - a) / d;
-    };
-
-    dist.icdf = function(p) {
-      return (p >= 0 && p <= 1) ? a + p * d : NaN;
-    };
-
+    if (max == null) {
+      max = (min == null ? 1 : min);
+      min = 0;
+    }
     return dist.min(min).max(max);
@@ -921,2 +1143,13 @@ }
   exports.bootstrapCI = bootstrapCI;
+  exports.cumulativeLogNormal = cumulativeLogNormal;
+  exports.cumulativeNormal = cumulativeNormal;
+  exports.cumulativeUniform = cumulativeUniform;
+  exports.densityLogNormal = densityLogNormal;
+  exports.densityNormal = densityNormal;
+  exports.densityUniform = densityUniform;
+  exports.dotbin = dotbin;
+  exports.quantileLogNormal = quantileLogNormal;
+  exports.quantileNormal = quantileNormal;
+  exports.quantileUniform = quantileUniform;
+  exports.quantiles = quantiles;
   exports.quartiles = quartiles;
@@ -926,2 +1159,3 @@ exports.randomInteger = integer;
   exports.randomLCG = lcg;
+  exports.randomLogNormal = lognormal;
   exports.randomMixture = mixture;
@@ -938,2 +1172,5 @@ exports.randomNormal = gaussian;
   exports.sampleCurve = sampleCurve;
+  exports.sampleLogNormal = sampleLogNormal;
+  exports.sampleNormal = sampleNormal;
+  exports.sampleUniform = sampleUniform;
   exports.setRandom = setRandom;
@@ -940,0 +1177,0 @@

build/vega-statistics.min.js

@@ -1,1 +0,1 @@
-!function(t,n){"object"==typeof exports&&"undefined"!=typeof module?n(exports,require("d3-array")):"function"==typeof define&&define.amd?define(["exports","d3-array"],n):n((t=t||self).vega={},t.d3)}(this,(function(t,n){"use strict";function*r(t,n){if(void 0===n)for(let n of t)null!=n&&(n=+n)>=n&&(yield n);else{let r=-1;for(let e of t)null!=(e=n(e,++r,t))&&(e=+e)>=e&&(yield e)}}function e(t,e){var o=Float64Array.from(r(t,e));return o.sort(n.ascending),[n.quantile(o,.25),n.quantile(o,.5),n.quantile(o,.75)]}function o(n,r){var e,o,a=NaN,u={mean:function(t){return arguments.length?(e=t||0,a=NaN,u):e},stdev:function(t){return arguments.length?(o=null==t?1:t,a=NaN,u):o},sample:function(){var n,r,u=0,f=0;if(a==a)return u=a,a=NaN,u;do{n=(u=2*t.random()-1)*u+(f=2*t.random()-1)*f}while(0===n||n>1);return r=Math.sqrt(-2*Math.log(n)/n),a=e+f*r*o,e+u*r*o},pdf:function(t){var n=Math.exp(Math.pow(t-e,2)/(-2*Math.pow(o,2)));return 1/(o*Math.sqrt(2*Math.PI))*n},cdf:function(t){var n,r=(t-e)/o,a=Math.abs(r);if(a>37)n=0;else{var u=Math.exp(-a*a/2);a<7.07106781186547?(n=u*((((((.0352624965998911*a+.700383064443688)*a+6.37396220353165)*a+33.912866078383)*a+112.079291497871)*a+221.213596169931)*a+220.206867912376),n/=((((((.0883883476483184*a+1.75566716318264)*a+16.064177579207)*a+86.7807322029461)*a+296.564248779674)*a+637.333633378831)*a+793.826512519948)*a+440.413735824752):n=u/(a+1/(a+2/(a+3/(a+4/(a+.65)))))/2.506628274631}return r>0?1-n:n},icdf:function(t){if(t<=0||t>=1)return NaN;var n=2*t-1,r=8*(Math.PI-3)/(3*Math.PI*(4-Math.PI)),a=2/(Math.PI*r)+Math.log(1-Math.pow(n,2))/2,u=Math.log(1-n*n)/r,f=(n>0?1:-1)*Math.sqrt(Math.sqrt(a*a-u)-a);return e+o*Math.SQRT2*f}};return u.mean(n).stdev(r)}function a(t){var r=t.length,o=e(t),a=(o[2]-o[0])/1.34;return 1.06*Math.min(Math.sqrt(n.variance(t)),a)*Math.pow(r,-.2)}function u(t,n,r,e){const o=e-t*t,a=Math.abs(o)<1e-24?0:(r-t*n)/o;return[n-a*t,a]}function f(t,n,r,e){t=t.filter(t=>{let e=n(t),o=r(t);return 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index.js

 export {default as bin} from './src/bin';
 export {default as bootstrapCI} from './src/bootstrapCI';
+export {default as dotbin} from './src/dotbin';
+export {default as quantiles} from './src/quantiles';
 export {default as quartiles} from './src/quartiles';
@@ -8,5 +10,24 @@ export {random, setRandom} from './src/random';
 export {default as randomKDE} from './src/kde';
+export {
+  default as randomLogNormal,
+  sampleLogNormal,
+  densityLogNormal,
+  cumulativeLogNormal,
+  quantileLogNormal
+} from './src/lognormal';
 export {default as randomMixture} from './src/mixture';
-export {default as randomNormal} from './src/normal';
-export {default as randomUniform} from './src/uniform';
+export {
+  default as randomNormal,
+  sampleNormal,
+  densityNormal,
+  cumulativeNormal,
+  quantileNormal
+} from './src/normal';
+export {
+  default as randomUniform,
+  sampleUniform,
+  densityUniform,
+  cumulativeUniform,
+  quantileUniform
+} from './src/uniform';
 export {default as regressionLinear} from './src/regression/linear';
@@ -13,0 +34,0 @@ export {default as regressionLog} from './src/regression/log';

package.json

 {
   "name": "vega-statistics",
-  "version": "1.5.0",
+  "version": "1.6.0",
   "description": "Statistical routines and probability distributions.",
@@ -27,5 +27,5 @@ "keywords": [
   "dependencies": {
-    "d3-array": "^2.0.3"
+    "d3-array": "^2.3.1"
   },
-  "gitHead": "9badf6d2d1490057f4010e3796189ca366878101"
+  "gitHead": "016e41e94f617acc1fe6d5eb3242b2646b5780c6"
 }

README.md

@@ -8,3 +8,4 @@ # vega-statistics
 - [Random Number Generation](#random-number-generation)
-- [Distributions](#distributions)
+- [Distribution Methods](#distribution-methods)
+- [Distribution Objects](#distribution-objects)
 - [Regression](#regression)
@@ -33,6 +34,82 @@ - [Statistics](#statistics)
 
-### Distributions
+### Distribution Methods
 
-Methods for sampling and calculating probability distributions. Each method takes a set of distributional parameters and returns a distribution object representing a random variable.
+Methods for sampling and calculating values for probability distributions.
 
+<a name="sampleNormal" href="#sampleNormal">#</a>
+vega.<b>sampleNormal</b>([<i>mean</i>, <i>stdev</i>])
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/normal.js "Source")
+
+Returns a sample from a univariate [normal (Gaussian) probability distribution](https://en.wikipedia.org/wiki/Normal_distribution) with specified *mean* and standard deviation *stdev*. If unspecified, the mean defaults to `0` and the standard deviation defaults to `1`.
+
+<a name="cumulativeNormal" href="#cumulativeNormal">#</a>
+vega.<b>cumulativeNormal</b>(value[, <i>mean</i>, <i>stdev</i>])
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/normal.js "Source")
+
+Returns the value of the [cumulative distribution function](https://en.wikipedia.org/wiki/Cumulative_distribution_function) at the given input domain *value* for a normal distribution with specified *mean* and standard deviation *stdev*. If unspecified, the mean defaults to `0` and the standard deviation defaults to `1`.
+
+<a name="densityNormal" href="#densityNormal">#</a>
+vega.<b>densityNormal</b>(value[, <i>mean</i>, <i>stdev</i>])
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/normal.js "Source")
+
+Returns the value of the [probability density function](https://en.wikipedia.org/wiki/Probability_density_function) at the given input domain *value*, for a normal distribution with specified *mean* and standard deviation *stdev*. If unspecified, the mean defaults to `0` and the standard deviation defaults to `1`.
+
+<a name="quantileNormal" href="#quantileNormal">#</a>
+vega.<b>quantileNormal</b>(probability[, <i>mean</i>, <i>stdev</i>])
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/normal.js "Source")
+
+Returns the quantile value (the inverse of the [cumulative distribution function](https://en.wikipedia.org/wiki/Cumulative_distribution_function)) for the given input *probability*, for a normal distribution with specified *mean* and standard deviation *stdev*. If unspecified, the mean defaults to `0` and the standard deviation defaults to `1`.
+
+<a name="sampleLogNormal" href="#sampleLogNormal">#</a>
+vega.<b>sampleLogNormal</b>([<i>mean</i>, <i>stdev</i>])
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/lognormal.js "Source")
+
+Returns a sample from a univariate [log-normal probability distribution](https://en.wikipedia.org/wiki/Log-normal_distribution) with specified log *mean* and log standard deviation *stdev*. If unspecified, the log mean defaults to `0` and the log standard deviation defaults to `1`.
+
+<a name="cumulativeLogNormal" href="#cumulativeNormal">#</a>
+vega.<b>cumulativeLogNormal</b>(value[, <i>mean</i>, <i>stdev</i>])
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/lognormal.js "Source")
+
+Returns the value of the [cumulative distribution function](https://en.wikipedia.org/wiki/Cumulative_distribution_function) at the given input domain *value* for a log-normal distribution with specified log *mean* and log standard deviation *stdev*. If unspecified, the log mean defaults to `0` and the log standard deviation defaults to `1`.
+
+<a name="densityLogNormal" href="#densityLogNormal">#</a>
+vega.<b>densityLogNormal</b>(value[, <i>mean</i>, <i>stdev</i>])
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/lognormal.js "Source")
+
+Returns the value of the [probability density function](https://en.wikipedia.org/wiki/Probability_density_function) at the given input domain *value*, for a log-normal distribution with specified log *mean* and log standard deviation *stdev*. If unspecified, the log mean defaults to `0` and the log standard deviation defaults to `1`.
+
+<a name="quantileLogNormal" href="#quantileLogNormal">#</a>
+vega.<b>quantileLogNormal</b>(probability[, <i>mean</i>, <i>stdev</i>])
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/lognormal.js "Source")
+
+Returns the quantile value (the inverse of the [cumulative distribution function](https://en.wikipedia.org/wiki/Cumulative_distribution_function)) for the given input *probability*, for a log-normal distribution with specified log *mean* and log standard deviation *stdev*. If unspecified, the log mean defaults to `0` and the log standard deviation defaults to `1`.
+
+<a name="sampleUniform" href="#sampleUniform">#</a>
+vega.<b>sampleUniform</b>([<i>min</i>, <i>max</i>])
+[<>](https://github.com/vega/vega-statistics/blob/master/src/uniform.js "Source")
+
+Returns a sample from a univariate [continuous uniform probability distribution](https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)) over the interval [*min*, *max*). If unspecified, *min* defaults to `0` and *max* defaults to `1`. If only one argument is provided, it is interpreted as the *max* value.
+
+<a name="cumulativeUniform" href="#cumulativeUniform">#</a>
+vega.<b>cumulativeUniform</b>(value[, <i>mean</i>, <i>stdev</i>])
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/uniform.js "Source")
+
+Returns the value of the [cumulative distribution function](https://en.wikipedia.org/wiki/Cumulative_distribution_function) at the given input domain *value* for a uniform distribution over the interval [*min*, *max*). If unspecified, *min* defaults to `0` and *max* defaults to `1`. If only one argument is provided, it is interpreted as the *max* value.
+
+<a name="densityUniform" href="#densityUniform">#</a>
+vega.<b>densityUniform</b>(value[, <i>mean</i>, <i>stdev</i>])
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/uniform.js "Source")
+
+Returns the value of the [probability density function](https://en.wikipedia.org/wiki/Probability_density_function) at the given input domain *value*,  for a uniform distribution over the interval [*min*, *max*). If unspecified, *min* defaults to `0` and *max* defaults to `1`. If only one argument is provided, it is interpreted as the *max* value.
+
+<a name="quantileUniform" href="#quantileUniform">#</a>
+vega.<b>quantileUniform</b>(probability[, <i>mean</i>, <i>stdev</i>])
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/uniform.js "Source")
+
+Returns the quantile value (the inverse of the [cumulative distribution function](https://en.wikipedia.org/wiki/Cumulative_distribution_function)) for the given input *probability*,  for a uniform distribution over the interval [*min*, *max*). If unspecified, *min* defaults to `0` and *max* defaults to `1`. If only one argument is provided, it is interpreted as the *max* value.
+
+### Distribution Objects
+
+Objects representing probability distributions, with methods for sampling and calculating values. Each method takes a set of distributional parameters and returns a distribution object representing a random variable.
+
 Distribution objects expose the following methods:
@@ -53,2 +130,10 @@
 
+<a name="randomLogNormal" href="#randomLogNormal">#</a>
+vega.<b>randomLogNormal</b>([<i>mean</i>, <i>stdev</i>])
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/lognormal.js "Source")
+
+Creates a distribution object representing a [log-normal probability distribution](https://en.wikipedia.org/wiki/Log-normal_distribution) with specified log *mean* and log standard deviation *stdev*. If unspecified, the log mean defaults to `0` and the log standard deviation defaults to `1`.
+
+Once created, *mean* and *stdev* values can be accessed or modified using the `mean` and `stdev` getter/setter methods.
+
 <a name="randomUniform" href="#randomUniform">#</a>
@@ -198,2 +283,14 @@ vega.<b>randomUniform</b>([<i>min</i>, <i>max</i>])
 
+<a name="dotbin" href="#dotbin">#</a>
+vega.<b>dotbin</b>(<i>sortedArray</i>, <i>step</i>[, <i>smooth</i>, <i>accessor</i>])
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/dotbin.js "Source")
+
+Calculates [dot plot](https://en.wikipedia.org/wiki/Dot_plot_%28statistics%29) bin locations for an input *sortedArray* of numerical values, and returns an array of bin locations with indices matching the input *sortedArray*. This method implements the ["dot density" algorithm of Wilkinson, 1999](https://www.cs.uic.edu/~wilkinson/Publications/dotplots.pdf). The *step* parameter determines the bin width: points within *step* values of an anchor point will be assigned the same bin location. The optional *smooth* parameter is a boolean value indicating if the bin locations should additionally be smoothed to reduce variance. An optional *accessor* function can be used to first extract numerical values from an array of input objects, and is equivalent to first calling `array.map(accessor)`. Any null, undefined, or NaN values should be removed prior to calling this method.
+
+<a name="quantiles" href="#quartiles">#</a>
+vega.<b>quantiles</b>(<i>array</i>, <i>p</i>[, <i>accessor</i>])
+[<>](https://github.com/vega/vega/blob/master/packages/vega-statistics/src/quartiles.js "Source")
+
+Given an *array* of numeric values and array *p* of probability thresholds in the range [0, 1], returns an array of p-[quantiles](https://en.wikipedia.org/wiki/Quantile). The return value is a array the same length as the input *p*. An optional *accessor* function can be used to first extract numerical values from an array of input objects, and is equivalent to first calling `array.map(accessor)`. This method ignores null, undefined and NaN values.
+
 <a name="quartiles" href="#quartiles">#</a>
@@ -200,0 +297,0 @@ vega.<b>quartiles</b>(<i>array</i>[, <i>accessor</i>])

src/normal.js

@@ -0,36 +1,15 @@
+import {SQRT2, SQRT2PI} from './constants';
 import {random} from './random';
 
-export default function(mean, stdev) {
-  var mu,
-      sigma,
-      next = NaN,
-      dist = {};
+let nextSample = NaN;
 
-  dist.mean = function(_) {
-    if (arguments.length) {
-      mu = _ || 0;
-      next = NaN;
-      return dist;
-    } else {
-      return mu;
-    }
-  };
+export function sampleNormal(mean, stdev) {
+  mean = mean || 0;
+  stdev = stdev == null ? 1 : stdev;
 
-  dist.stdev = function(_) {
-    if (arguments.length) {
-      sigma = _ == null ? 1 : _;
-      next = NaN;
-      return dist;
-    } else {
-      return sigma;
-    }
-  };
-
-  dist.sample = function() {
-    var x = 0, y = 0, rds, c;
-    if (next === next) {
-      x = next;
-      next = NaN;
-      return x;
-    }
+  let x = 0, y = 0, rds, c;
+  if (nextSample === nextSample) {
+    x = nextSample;
+    nextSample = NaN;
+  } else {
     do {
@@ -42,61 +21,171 @@ x = random() * 2 - 1;
     c = Math.sqrt(-2 * Math.log(rds) / rds); // Box-Muller transform
-    next = mu + y * c * sigma;
-    return mu + x * c * sigma;
-  };
+    x *= c;
+    nextSample = y * c;
+  }
+  return mean + x * stdev;
+}
 
-  dist.pdf = function(x) {
-    var exp = Math.exp(Math.pow(x-mu, 2) / (-2 * Math.pow(sigma, 2)));
-    return (1 / (sigma * Math.sqrt(2*Math.PI))) * exp;
-  };
+export function densityNormal(value, mean, stdev) {
+  stdev = stdev == null ? 1 : stdev;
+  const z = (value - (mean || 0)) / stdev;
+  return Math.exp(-0.5 * z * z) / (stdev * SQRT2PI);
+}
 
-  // Approximation from West (2009)
-  // Better Approximations to Cumulative Normal Functions
-  dist.cdf = function(x) {
-    var cd,
-        z = (x - mu) / sigma,
-        Z = Math.abs(z);
-    if (Z > 37) {
-      cd = 0;
+// Approximation from West (2009)
+// Better Approximations to Cumulative Normal Functions
+export function cumulativeNormal(value, mean, stdev) {
+  mean = mean || 0;
+  stdev = stdev == null ? 1 : stdev;
+
+  let cd,
+      z = (value - mean) / stdev,
+      Z = Math.abs(z);
+
+  if (Z > 37) {
+    cd = 0;
+  } else {
+    let sum, exp = Math.exp(-Z * Z / 2);
+    if (Z < 7.07106781186547) {
+      sum = 3.52624965998911e-02 * Z + 0.700383064443688;
+      sum = sum * Z + 6.37396220353165;
+      sum = sum * Z + 33.912866078383;
+      sum = sum * Z + 112.079291497871;
+      sum = sum * Z + 221.213596169931;
+      sum = sum * Z + 220.206867912376;
+      cd = exp * sum;
+      sum = 8.83883476483184e-02 * Z + 1.75566716318264;
+      sum = sum * Z + 16.064177579207;
+      sum = sum * Z + 86.7807322029461;
+      sum = sum * Z + 296.564248779674;
+      sum = sum * Z + 637.333633378831;
+      sum = sum * Z + 793.826512519948;
+      sum = sum * Z + 440.413735824752;
+      cd = cd / sum;
     } else {
-      var sum, exp = Math.exp(-Z*Z/2);
-      if (Z < 7.07106781186547) {
-        sum = 3.52624965998911e-02 * Z + 0.700383064443688;
-        sum = sum * Z + 6.37396220353165;
-        sum = sum * Z + 33.912866078383;
-        sum = sum * Z + 112.079291497871;
-        sum = sum * Z + 221.213596169931;
-        sum = sum * Z + 220.206867912376;
-        cd = exp * sum;
-        sum = 8.83883476483184e-02 * Z + 1.75566716318264;
-        sum = sum * Z + 16.064177579207;
-        sum = sum * Z + 86.7807322029461;
-        sum = sum * Z + 296.564248779674;
-        sum = sum * Z + 637.333633378831;
-        sum = sum * Z + 793.826512519948;
-        sum = sum * Z + 440.413735824752;
-        cd = cd / sum;
-      } else {
-        sum = Z + 0.65;
-        sum = Z + 4 / sum;
-        sum = Z + 3 / sum;
-        sum = Z + 2 / sum;
-        sum = Z + 1 / sum;
-        cd = exp / sum / 2.506628274631;
-      }
+      sum = Z + 0.65;
+      sum = Z + 4 / sum;
+      sum = Z + 3 / sum;
+      sum = Z + 2 / sum;
+      sum = Z + 1 / sum;
+      cd = exp / sum / 2.506628274631;
     }
-    return z > 0 ? 1 - cd : cd;
-  };
+  }
+  return z > 0 ? 1 - cd : cd;
+}
 
-  // Approximation of Probit function using inverse error function.
-  dist.icdf = function(p) {
-    if (p <= 0 || p >= 1) return NaN;
-    var x = 2*p - 1,
-        v = (8 * (Math.PI - 3)) / (3 * Math.PI * (4-Math.PI)),
-        a = (2 / (Math.PI*v)) + (Math.log(1 - Math.pow(x,2)) / 2),
-        b = Math.log(1 - (x*x)) / v,
-        s = (x > 0 ? 1 : -1) * Math.sqrt(Math.sqrt((a*a) - b) - a);
-    return mu + sigma * Math.SQRT2 * s;
-  };
+// Approximation of Probit function using inverse error function.
+export function quantileNormal(p, mean, stdev) {
+  if (p < 0 || p > 1) return NaN;
+  return (mean || 0) + (stdev == null ? 1 : stdev) * SQRT2 * erfinv(2 * p - 1);
+}
 
+// Approximate inverse error function. Implementation from "Approximating
+// the erfinv function" by Mike Giles, GPU Computing Gems, volume 2, 2010.
+// Ported from Apache Commons Math, http://www.apache.org/licenses/LICENSE-2.0
+function erfinv(x) {
+  // beware that the logarithm argument must be
+  // commputed as (1.0 - x) * (1.0 + x),
+  // it must NOT be simplified as 1.0 - x * x as this
+  // would induce rounding errors near the boundaries +/-1
+  let w = - Math.log((1 - x) * (1 + x)), p;
+
+  if (w < 6.25) {
+      w -= 3.125;
+      p =  -3.6444120640178196996e-21;
+      p =   -1.685059138182016589e-19 + p * w;
+      p =   1.2858480715256400167e-18 + p * w;
+      p =    1.115787767802518096e-17 + p * w;
+      p =   -1.333171662854620906e-16 + p * w;
+      p =   2.0972767875968561637e-17 + p * w;
+      p =   6.6376381343583238325e-15 + p * w;
+      p =  -4.0545662729752068639e-14 + p * w;
+      p =  -8.1519341976054721522e-14 + p * w;
+      p =   2.6335093153082322977e-12 + p * w;
+      p =  -1.2975133253453532498e-11 + p * w;
+      p =  -5.4154120542946279317e-11 + p * w;
+      p =    1.051212273321532285e-09 + p * w;
+      p =  -4.1126339803469836976e-09 + p * w;
+      p =  -2.9070369957882005086e-08 + p * w;
+      p =   4.2347877827932403518e-07 + p * w;
+      p =  -1.3654692000834678645e-06 + p * w;
+      p =  -1.3882523362786468719e-05 + p * w;
+      p =    0.0001867342080340571352 + p * w;
+      p =  -0.00074070253416626697512 + p * w;
+      p =   -0.0060336708714301490533 + p * w;
+      p =      0.24015818242558961693 + p * w;
+      p =       1.6536545626831027356 + p * w;
+  } else if (w < 16.0) {
+      w = Math.sqrt(w) - 3.25;
+      p =   2.2137376921775787049e-09;
+      p =   9.0756561938885390979e-08 + p * w;
+      p =  -2.7517406297064545428e-07 + p * w;
+      p =   1.8239629214389227755e-08 + p * w;
+      p =   1.5027403968909827627e-06 + p * w;
+      p =   -4.013867526981545969e-06 + p * w;
+      p =   2.9234449089955446044e-06 + p * w;
+      p =   1.2475304481671778723e-05 + p * w;
+      p =  -4.7318229009055733981e-05 + p * w;
+      p =   6.8284851459573175448e-05 + p * w;
+      p =   2.4031110387097893999e-05 + p * w;
+      p =   -0.0003550375203628474796 + p * w;
+      p =   0.00095328937973738049703 + p * w;
+      p =   -0.0016882755560235047313 + p * w;
+      p =    0.0024914420961078508066 + p * w;
+      p =   -0.0037512085075692412107 + p * w;
+      p =     0.005370914553590063617 + p * w;
+      p =       1.0052589676941592334 + p * w;
+      p =       3.0838856104922207635 + p * w;
+  } else if (Number.isFinite(w)) {
+      w = Math.sqrt(w) - 5.0;
+      p =  -2.7109920616438573243e-11;
+      p =  -2.5556418169965252055e-10 + p * w;
+      p =   1.5076572693500548083e-09 + p * w;
+      p =  -3.7894654401267369937e-09 + p * w;
+      p =   7.6157012080783393804e-09 + p * w;
+      p =  -1.4960026627149240478e-08 + p * w;
+      p =   2.9147953450901080826e-08 + p * w;
+      p =  -6.7711997758452339498e-08 + p * w;
+      p =   2.2900482228026654717e-07 + p * w;
+      p =  -9.9298272942317002539e-07 + p * w;
+      p =   4.5260625972231537039e-06 + p * w;
+      p =  -1.9681778105531670567e-05 + p * w;
+      p =   7.5995277030017761139e-05 + p * w;
+      p =  -0.00021503011930044477347 + p * w;
+      p =  -0.00013871931833623122026 + p * w;
+      p =       1.0103004648645343977 + p * w;
+      p =       4.8499064014085844221 + p * w;
+  } else {
+      p = Infinity;
+  }
+
+  return p * x;
+}
+
+export default function(mean, stdev) {
+  var mu,
+      sigma,
+      dist = {
+        mean: function(_) {
+          if (arguments.length) {
+            mu = _ || 0;
+            return dist;
+          } else {
+            return mu;
+          }
+        },
+        stdev: function(_) {
+          if (arguments.length) {
+            sigma = _ == null ? 1 : _;
+            return dist;
+          } else {
+            return sigma;
+          }
+        },
+        sample: () => sampleNormal(mu, sigma),
+        pdf: value => densityNormal(value, mu, sigma),
+        cdf: value => cumulativeNormal(value, mu, sigma),
+        icdf: p => quantileNormal(p, mu, sigma)
+      };
+
   return dist.mean(mean).stdev(stdev);
 }

src/quartiles.js

@@ -1,16 +0,5 @@
-import numbers from './numbers';
-import {quantile, ascending} from 'd3-array';
+import quantiles from './quantiles';
 
 export default function(array, f) {
-  var values = Float64Array.from(numbers(array, f));
-
-  // don't depend on return value from typed array sort call
-  // protects against undefined sort results in Safari (vega/vega-lite#4964)
-  values.sort(ascending);
-
-  return [
-    quantile(values, 0.25),
-    quantile(values, 0.50),
-    quantile(values, 0.75)
-  ];
+  return quantiles(array, [0.25, 0.50, 0.75], f);
 }

src/uniform.js

 import {random} from './random';
 
-export default function(min, max) {
+export function sampleUniform(min, max) {
   if (max == null) {
@@ -8,43 +8,59 @@ max = (min == null ? 1 : min);
   }
+  return min + (max - min) * random();
+}
 
-  var dist = {},
-      a, b, d;
+export function densityUniform(value, min, max) {
+  if (max == null) {
+    max = (min == null ? 1 : min);
+    min = 0;
+  }
+  return (value >= min && value <= max) ? 1 / (max - min) : 0;
+}
 
-  dist.min = function(_) {
-    if (arguments.length) {
-      a = _ || 0;
-      d = b - a;
-      return dist;
-    } else {
-      return a;
-    }
-  };
+export function cumulativeUniform(value, min, max) {
+  if (max == null) {
+    max = (min == null ? 1 : min);
+    min = 0;
+  }
+  return value < min ? 0 : value > max ? 1 : (value - min) / (max - min);
+}
 
-  dist.max = function(_) {
-    if (arguments.length) {
-      b = _ || 0;
-      d = b - a;
-      return dist;
-    } else {
-      return b;
-    }
-  };
+export function quantileUniform(p, min, max) {
+  if (max == null) {
+    max = (min == null ? 1 : min);
+    min = 0;
+  }
+  return (p >= 0 && p <= 1) ? min + p * (max - min) : NaN;
+}
 
-  dist.sample = function() {
-    return a + d * random();
-  };
+export default function(min, max) {
+  var a, b,
+      dist = {
+        min: function(_) {
+          if (arguments.length) {
+            a = _ || 0;
+            return dist;
+          } else {
+            return a;
+          }
+        },
+        max: function(_) {
+          if (arguments.length) {
+            b = _ == null ? 1 : _;
+            return dist;
+          } else {
+            return b;
+          }
+        },
+        sample: () => sampleUniform(a, b),
+        pdf: value => densityUniform(value, a, b),
+        cdf: value => cumulativeUniform(value, a, b),
+        icdf: p => quantileUniform(p, a, b)
+      };
 
-  dist.pdf = function(x) {
-    return (x >= a && x <= b) ? 1 / d : 0;
-  };
-
-  dist.cdf = function(x) {
-    return x < a ? 0 : x > b ? 1 : (x - a) / d;
-  };
-
-  dist.icdf = function(p) {
-    return (p >= 0 && p <= 1) ? a + p * d : NaN;
-  };
-
+  if (max == null) {
+    max = (min == null ? 1 : min);
+    min = 0;
+  }
   return dist.min(min).max(max);
 }

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Number of package files

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increased by14.29%

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increased by27.53%

Number of lines in readme file

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increased by48.5%

Dependency changes

• Updatedd3-array@^2.3.1