{
"$schema": "https://vega.github.io/schema/vega-lite/v5.json",
"hconcat": [
{
"title": "Normal Distribution PDF (Mean=1, SD=2)",
"width": 200,
"height": 200,
"data": {
"sequence": {
"start": -5,
"stop": 7,
"step": 0.1,
"as": "x"
}
},
"transform": [
{
"calculate": "exp(-0.5 * pow((datum.x - 1) / 2, 2)) / (2 * sqrt(2 * PI))",
"as": "normal_pdf"
}
],
"mark": {
"type": "line",
"point": false
},
"encoding": {
"x": {
"field": "x",
"type": "quantitative",
"title": "x"
},
"y": {
"field": "normal_pdf",
"type": "quantitative",
"title": "Density"
}
}
},
{
"title": "Random Sample from N(1,2)",
"width": 200,
"height": 200,
"data": {
"sequence": {
"start": 1,
"stop": 101,
"step": 1,
"as": "index"
}
},
"transform": [
{
"calculate": "sampleNormal(1, 2)",
"as": "random_normal"
}
],
"mark": "point",
"encoding": {
"x": {
"field": "index",
"type": "quantitative",
"title": "Index"
},
"y": {
"field": "random_normal",
"type": "quantitative",
"title": "Uniform Value"
}
}
},
{
"title": "Histogram of 100 Samples from N(1, 2)",
"width": 200,
"height": 200,
"data": {
"sequence": {
"start": 1,
"stop": 101,
"step": 1,
"as": "index"
}
},
"transform": [
{
"calculate": "1 + 2 * sampleNormal(0, 1)",
"as": "sample_normal_50"
}
],
"mark": "bar",
"encoding": {
"x": {
"bin": {
"maxbins": 20
},
"field": "sample_normal_50",
"type": "quantitative",
"title": "Value"
},
"y": {
"aggregate": "count",
"type": "quantitative",
"title": "Frequency"
}
}
},
{
"title": "Histogram of 10,000 Samples from N(1, 2)",
"width": 200,
"height": 200,
"data": {
"sequence": {
"start": 1,
"stop": 10001,
"step": 1,
"as": "index"
}
},
"transform": [
{
"calculate": "1 + 2 * sampleNormal(0, 1)",
"as": "sample_normal_1000"
}
],
"mark": "bar",
"encoding": {
"x": {
"bin": {
"maxbins": 50
},
"field": "sample_normal_1000",
"type": "quantitative",
"title": "Value"
},
"y": {
"aggregate": "count",
"type": "quantitative",
"title": "Frequency"
}
}
}
]
}