{
"$schema": "https://vega.github.io/schema/vega-lite/v5.17.0.json",
"config": {
"view": {
"continuousWidth": 300,
"continuousHeight": 300
}
},
"data": {
"sequence": {
"start": 0,
"stop": 4,
"step": 0.1,
"as": "Loss"
}
},
"transform": [
{
"calculate": "densityLogNormal(datum.Loss, 0, 0.5)",
"as": "Density"
}
],
"layer": [
{
"mark": {
"type": "line",
"color": "blue"
},
"encoding": {
"x": {
"field": "Loss",
"title": "Loss",
"type": "quantitative"
},
"y": {
"field": "Density",
"title": "Density",
"type": "quantitative"
}
}
},
{
"transform": [
{
"filter": "datum.Loss >= 2.2857142857142856 && datum.Loss <= 4"
}
],
"mark": {
"type": "area",
"color": "red",
"opacity": 0.3
},
"encoding": {
"x": {
"field": "Loss",
"type": "quantitative"
},
"y": {
"field": "Density",
"type": "quantitative"
}
}
},
{
"data": {
"values": [
{
"Loss": 1.1331484530668263
}
]
},
"mark": {
"type": "rule",
"color": "green"
},
"encoding": {
"x": {
"field": "Loss",
"type": "quantitative"
}
}
},
{
"data": {
"values": [
{
"Loss": 2.276016608514317
}
]
},
"mark": {
"type": "rule",
"color": "red",
"strokeDash": [
3,
3
]
},
"encoding": {
"x": {
"field": "Loss",
"type": "quantitative"
}
}
},
{
"data": {
"values": [
{
"Loss": 2.8585912953125416
}
]
},
"mark": {
"type": "rule",
"color": "red"
},
"encoding": {
"x": {
"field": "Loss",
"type": "quantitative"
}
}
},
{
"data": {
"values": [
{
"x": 1.1331484530668263,
"y": 0.2
},
{
"x": 2.276016608514317,
"y": 0.2
}
]
},
"mark": {
"type": "line",
"color": "blue",
"strokeWidth": 2
},
"encoding": {
"x": {
"field": "x",
"type": "quantitative"
},
"y": {
"field": "y",
"type": "quantitative"
}
}
},
{
"data": {
"values": [
{
"x": 1.1331484530668263,
"y": 0.3
},
{
"x": 2.8585912953125416,
"y": 0.3
}
]
},
"mark": {
"type": "line",
"color": "blue",
"strokeWidth": 2
},
"encoding": {
"x": {
"field": "x",
"type": "quantitative"
},
"y": {
"field": "y",
"type": "quantitative"
}
}
},
{
"data": {
"values": [
{
"x": 1.1331484530668263,
"y": 0.2,
"angle": 180
},
{
"x": 2.276016608514317,
"y": 0.2,
"angle": 0
},
{
"x": 1.1331484530668263,
"y": 0.3,
"angle": 180
},
{
"x": 2.8585912953125416,
"y": 0.3,
"angle": 0
}
]
},
"mark": {
"type": "point",
"color": "blue",
"shape": "triangle",
"size": 100
},
"encoding": {
"angle": {
"field": "angle",
"type": "quantitative"
},
"x": {
"field": "x",
"type": "quantitative"
},
"y": {
"field": "y",
"type": "quantitative"
}
}
},
{
"data": {
"values": [
{
"Loss": 1.4822456789483234,
"Density": 0.22,
"label": "VaR = 1.14"
},
{
"Loss": 1.735539021034508,
"Density": 0.32,
"label": "CVaR = 1.73"
}
]
},
"mark": {
"type": "text",
"align": "left",
"angle": 0,
"baseline": "middle",
"color": "blue",
"dx": 5,
"dy": 0
},
"encoding": {
"text": {
"field": "label",
"type": "nominal"
},
"x": {
"field": "Loss",
"type": "quantitative"
},
"y": {
"field": "Density",
"type": "quantitative"
}
}
},
{
"data": {
"values": [
{
"Loss": 1.1331484530668263,
"Density": 0.72,
"label": "Mean = 1.13"
},
{
"Loss": 2.276016608514317,
"Density": 0.78,
"label": "CL@95% = 2.28"
},
{
"Loss": 2.8585912953125416,
"Density": 0.84,
"label": "CCL@95% = 2.86"
}
]
},
"mark": {
"type": "text",
"align": "left",
"angle": 0,
"baseline": "middle",
"color": "black",
"dx": 5,
"dy": 0
},
"encoding": {
"text": {
"field": "label",
"type": "nominal"
},
"x": {
"field": "Loss",
"type": "quantitative"
},
"y": {
"field": "Density",
"type": "quantitative"
}
}
}
],
"title": "Probability Density Function (PDF) of Lognormal Distribution (μ=0, σ=0.5)"
}