# Probability Density Example

Visual comparison of estimated probability distributions for a sample of numeric values: a normal (Gaussian) distribution parameterized by the mean and standard deviation, and a kernel density estimate. This example supports estimates of either probability density functions (pdf) or cumulative distribution functions (cdf), using Vega’s density transform.

### Vega JSON Specification <>

``````{
"\$schema": "https://vega.github.io/schema/vega/v5.json",
"description": "Area chart using density estimation to show a probability density or cumulative distribution.",
"width": 500,
"height": 100,

"signals": [
{ "name": "bandwidth", "value": 0,
"bind": {"input": "range", "min": 0, "max": 0.1, "step": 0.001} },
{ "name": "method", "value": "pdf",
"bind": {"input": "radio", "options": ["pdf", "cdf"]} }
],

"data": [
{
"name": "points",
"url": "data/normal-2d.json"
},
{
"name": "summary",
"source": "points",
"transform": [
{
"type": "aggregate",
"fields": ["u", "u"],
"ops": ["mean", "stdev"],
"as": ["mean", "stdev"]
}
]
},
{
"name": "density",
"source": "points",
"transform": [
{
"type": "density",
"extent": {"signal": "domain('xscale')"},
"method": {"signal": "method"},
"distribution": {
"function": "kde",
"field": "u",
"bandwidth": {"signal": "bandwidth"}
}
}
]
},
{
"name": "normal",
"transform": [
{
"type": "density",
"extent": {"signal": "domain('xscale')"},
"method": {"signal": "method"},
"distribution": {
"function": "normal",
"mean": {"signal": "data('summary')[0].mean"},
"stdev": {"signal": "data('summary')[0].stdev"}
}
}
]
}
],

"scales": [
{
"name": "xscale",
"type": "linear",
"range": "width",
"domain": {"data": "points", "field": "u"},
"nice": true
},
{
"name": "yscale",
"type": "linear",
"range": "height", "round": true,
"domain": {
"fields": [
{"data": "density", "field": "density"},
{"data": "normal", "field": "density"}
]
}
},
{
"name": "color",
"type": "ordinal",
"domain": ["Normal Estimate", "Kernel Density Estimate"],
"range": ["#444", "steelblue"]
}
],

"axes": [
{"orient": "bottom", "scale": "xscale", "zindex": 1}
],

"legends": [
{"orient": "top-left", "fill": "color", "offset": 0, "zindex": 1}
],

"marks": [
{
"type": "area",
"from": {"data": "density"},
"encode": {
"update": {
"x": {"scale": "xscale", "field": "value"},
"y": {"scale": "yscale", "field": "density"},
"y2": {"scale": "yscale", "value": 0},
"fill": {"signal": "scale('color', 'Kernel Density Estimate')"}
}
}
},
{
"type": "line",
"from": {"data": "normal"},
"encode": {
"update": {
"x": {"scale": "xscale", "field": "value"},
"y": {"scale": "yscale", "field": "density"},
"stroke": {"signal": "scale('color', 'Normal Estimate')"},
"strokeWidth": {"value": 2}
}
}
},
{
"type": "rect",
"from": {"data": "points"},
"encode": {
"enter": {
"x": {"scale": "xscale", "field": "u"},
"width": {"value": 1},
"y": {"value": 25, "offset": {"signal": "height"}},
"height": {"value": 5},
"fill": {"value": "steelblue"},
"fillOpacity": {"value": 0.4}
}
}
}
]
}

``````