tomgp
9/26/2013 - 8:23 PM

## Discrete Gaussian distribution

Discrete Gaussian distribution

``````<html>
<title>Discrete Gausian</title>
<!-- general -->
<style type="text/css">
body{
font-family: sans-serif;
}
</style>
<!--bars-->
<style type="text/css">
.distribution-bar{
fill:#333;
stroke:#fff;
}

</style>
<!--slider-->
<style type="text/css">
.axis {
font: 10px sans-serif;
-webkit-user-select: none;
-moz-user-select: none;
user-select: none;
}

.axis .domain {
fill: none;
stroke: #000;
stroke-opacity: .3;
stroke-width: 10px;
stroke-linecap: round;
}

.axis .halo {
fill: none;
stroke: #ddd;
stroke-width: 8px;
stroke-linecap: round;
}

.slider .handle {
fill: #fff;
stroke: #000;
stroke-opacity: .5;
stroke-width: 1.25px;
pointer-events: none;
}
</style>
<body>
<div id='distribution-chart'><svg id='gaussian'></svg></div>
<p>Set the variance:</p>
<div id='distribution-control'><svg id='variance-slider'></svg></div>
</body>
<script src="http://d3js.org/d3.v3.min.js"></script>
<script type="text/javascript" src="gaussian.js"></script>
<script type="text/javascript">
'use strict'

function discreteGausian( mean, variance, resolution ){
var mean = 0,
distribution = new Gaussian(mean, variance),
discretePDF = 1,
oldCDF = distribution.cdf(mean - (resolution/2)),
discreteDistribution = [],
sliceThreshold = 0.001,
jobDone = false,
i = (mean + resolution/2);

while(!jobDone){
var newCDF = distribution.cdf( i );
var slice = newCDF - oldCDF;
discreteDistribution.push( slice );
if(discreteDistribution.length  > 1 ){
discreteDistribution.unshift( slice );
}
if(slice < sliceThreshold){
jobDone = true;
}
oldCDF = newCDF;
i += resolution;
}
return discreteDistribution;
}

var height = 300,
sliderHeight = 150,
width = 700;

var varianceSliderScale = d3.scale.linear()
.domain([0.01, 30])
.range([0, width-60])
.clamp(true);

d3.selectAll('svg')
.attr('width',width)
.attr('height',height);

drawDistribution('#gaussian', discreteGausian(0, 2, 1));
drawControl('#variance-slider', varianceSliderScale, changeVariance);

function changeVariance(v){
if(v>0){
drawDistribution('#gaussian', discreteGausian(0, v, 1));
}
}

function drawControl(svgSelector, scale, callback){
var margin = {top:10,left:30,bottom:30,right:30};
var brush = d3.svg.brush()
.x(scale)
.extent([0, 0])
.on("brush", brushed);

var svg = d3.select(svgSelector)
.attr('width', width)
.attr('height', sliderHeight)
.append('g').attr('transform', 'translate('+margin.left+','+margin.top+')');

svg.append("g")
.attr("class", "x axis")
.attr("transform", "translate(0," + height / 2 + ")")
.call(d3.svg.axis()
.scale(scale)
.orient("bottom")
//				.tickFormat(function(d) { return d; })
.tickSize(0)
.select(".domain")
.select(function() { return this.parentNode.appendChild(this.cloneNode(true)); })
.attr("class", "halo");

var slider = svg.append("g")
.attr("class", "slider")
.call(brush);

slider.selectAll(".extent,.resize")
.remove();

slider.select(".background")
.attr("height", height);

var handle = slider.append("circle")
.attr("class", "handle")
.attr("transform", "translate(0," + sliderHeight / 2 + ")")
.attr("r", 9);

slider
.call(brush.event);

function brushed() {
var value = brush.extent()[0];
if (d3.event.sourceEvent) { // not a programmatic event
value = scale.invert(d3.mouse(this)[0]);
brush.extent([value, value]);
}
handle.attr("cx", scale(value));
callback(value);
}

}

function drawDistribution(svgSelector, distribution){
var x = d3.scale.linear()
.domain([0, distribution.length])
.range([0, width]);
var y = d3.scale.linear()
.domain([0, d3.max(distribution)])
.range([0, height]);

var group = d3.select(svgSelector).selectAll('rect')
.data(distribution)

group.enter().append('rect')
.attr('x',function(d,i){
return width;
})
.attr('y',function(d){
return height-y(d);
})
.attr('height',function(d){
return y(d);
})
.attr('width', function(){
return x(1);
})
.attr('class','distribution-bar');

group.transition()
.attr('x',function(d,i){
console.log('c');
return x(i);
})
.attr('y',function(d){
return height-y(d);
})
.attr('height',function(d){
return y(d);
})
.attr('width', function(){
return x(1);
});

group.exit().remove();
}

</script>
</html>``````
``````// Models the normal distribution

var Gaussian = function(mean, variance) {
if (variance <= 0) {
throw new Error('Variance must be > 0 (but was ' + variance + ')');
}

var stddev = Math.sqrt(variance);
var precision = 1 / variance;
var precisionmean = precision * mean;

// Complementary error function
// From Numerical Recipes in C 2e p221
var erfc = function(x) {
var z = Math.abs(x);
var t = 1 / (1 + z / 2);
var r = t * Math.exp(-z * z - 1.26551223 + t * (1.00002368 +
t * (0.37409196 + t * (0.09678418 + t * (-0.18628806 +
t * (0.27886807 + t * (-1.13520398 + t * (1.48851587 +
t * (-0.82215223 + t * 0.17087277)))))))))
return x >= 0 ? r : 2 - r;
};

// Inverse complementary error function
// From Numerical Recipes 3e p265
var ierfc = function(x) {
if (x >= 2) { return -100; }
if (x <= 0) { return 100; }

var xx = (x < 1) ? x : 2 - x;
var t = Math.sqrt(-2 * Math.log(xx / 2));

var r = -0.70711 * ((2.30753 + t * 0.27061) /
(1 + t * (0.99229 + t * 0.04481)) - t);

for (var j = 0; j < 2; j++) {
var err = erfc(r) - xx;
r += err / (1.12837916709551257 * Math.exp(-(r * r)) - r * err);
}

return (x < 1) ? r : -r;
};

// Construct a new distribution from the precision and precisionmean
var fromPrecisionMean = function(precision, precisionmean) {
var mean = precisionmean / precision;
var variance = 1 / precision;
return new Gaussian(mean, variance);
};

return {
mean: mean,
variance: variance,
standardDeviation: stddev,

precision: precision,
precisionmean: precisionmean,

// Probability density function
pdf: function(x) {
var m = stddev * Math.sqrt(2 * Math.PI);
var e = Math.exp(-Math.pow(x - mean, 2) / (2 * variance));
return e / m;
},

// Cumulative density function
cdf: function(x) {
return 0.5 * erfc(-(x - mean) / (stddev * Math.sqrt(2)));
},

// Percent point function (inverse of cdf)
ppf: function(x) {
return mean - stddev * Math.sqrt(2) * ierfc(2 * x);
},

// Product distribution of this and d
mul: function(d) {
return fromPrecisionMean(
precision + d.precision,
precisionmean  + d.precisionmean);
},

// Quotient distribution of this and d
div: function(d) {
return fromPrecisionMean(
precision - d.precision,
precisionmean  - d.precisionmean);
}
};
};

/*module.exports = function(mean, variance) {
return new Gaussian(mean, variance);
};*/

/*
https://github.com/errcw/gaussian

Permission is hereby granted, free of charge, to any person obtaining a copy of
this software and associated documentation files (the "Software"), to deal in
the Software without restriction, including without limitation the rights to
use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
of the Software, and to permit persons to whom the Software is furnished to do
so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

*/``````

Make a Discrete Gaussian distribution

for genererating a PDF this package Also, this was helpfull