# Empirical Cumulative Distribution Plots in Python

How to add empirical cumulative distribution function (ECDF) plots.

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### Overview¶

Empirical cumulative distribution function plots are a way to visualize the distribution of a variable, and Plotly Express has a built-in function, px.ecdf() to generate such plots. Plotly Express is the easy-to-use, high-level interface to Plotly, which operates on a variety of types of data and produces easy-to-style figures.

Alternatives to ECDF plots for visualizing distributions include histograms, violin plots, box plots and strip charts.

### Simple ECDF Plots¶

Providing a single column to the x variable yields a basic ECDF plot.

In [1]:
import plotly.express as px
df = px.data.tips()
fig = px.ecdf(df, x="total_bill")
fig.show()


Providing multiple columns leverage's Plotly Express' wide-form data support to show multiple variables on the same plot.

In [2]:
import plotly.express as px
df = px.data.tips()
fig = px.ecdf(df, x=["total_bill", "tip"])
fig.show()


It is also possible to map another variable to the color dimension of a plot.

In [3]:
import plotly.express as px
df = px.data.tips()
fig = px.ecdf(df, x="total_bill", color="sex")
fig.show()


### Configuring the Y axis¶

By default, the Y axis shows probability, but it is also possible to show raw counts by setting the ecdfnorm argument to None or to show percentages by setting it to percent.

In [4]:
import plotly.express as px
df = px.data.tips()
fig = px.ecdf(df, x="total_bill", color="sex", ecdfnorm=None)
fig.show()


If a y value is provided, the Y axis is set to the sum of y rather than counts.

In [5]:
import plotly.express as px
df = px.data.tips()
fig = px.ecdf(df, x="total_bill", y="tip", color="sex", ecdfnorm=None)
fig.show()


### Reversed and Complementary CDF plots¶

By default, the Y value represents the fraction of the data that is at or below the value on on the X axis. Setting ecdfmode to "reversed" reverses this, with the Y axis representing the fraction of the data at or above the X value. Setting ecdfmode to "complementary" plots 1-ECDF, meaning that the Y values represent the fraction of the data above the X value.

In standard mode (the default), the right-most point is at 1 (or the total count/sum, depending on ecdfnorm) and the right-most point is above 0.

In [6]:
import plotly.express as px
fig = px.ecdf(df, x=[1,2,3,4], markers=True, ecdfmode="standard",
title="ecdfmode='standard' (Y=fraction at or below X value, this the default)")
fig.show()


In reversed mode, the right-most point is at 1 (or the total count/sum, depending on ecdfnorm) and the left-most point is above 0.

In [7]:
import plotly.express as px
fig = px.ecdf(df, x=[1,2,3,4], markers=True, ecdfmode="reversed",
title="ecdfmode='reversed' (Y=fraction at or above X value)")
fig.show()


In complementary mode, the right-most point is at 0 and no points are at 1 (or the total count/sum) per the definition of the CCDF as 1-ECDF, which has no point at 0.

In [8]:
import plotly.express as px
fig = px.ecdf(df, x=[1,2,3,4], markers=True, ecdfmode="complementary",
title="ecdfmode='complementary' (Y=fraction above X value)")
fig.show()


### Orientation¶

By default, plots are oriented vertically (i.e. the variable is on the X axis and counted/summed upwards), but this can be overridden with the orientation argument.

In [9]:
import plotly.express as px
df = px.data.tips()
fig = px.ecdf(df, x="total_bill", y="tip", color="sex", ecdfnorm=None, orientation="h")
fig.show()


### Markers and/or Lines¶

ECDF Plots can be configured to show lines and/or markers.

In [10]:
import plotly.express as px
df = px.data.tips()
fig = px.ecdf(df, x="total_bill", color="sex", markers=True)
fig.show()

In [11]:
import plotly.express as px
df = px.data.tips()
fig = px.ecdf(df, x="total_bill", color="sex", markers=True, lines=False)
fig.show()


### Marginal Plots¶

ECDF plots also support marginal plots

In [12]:
import plotly.express as px
df = px.data.tips()
fig = px.ecdf(df, x="total_bill", color="sex", markers=True, lines=False, marginal="histogram")
fig.show()

In [13]:
import plotly.express as px
df = px.data.tips()
fig = px.ecdf(df, x="total_bill", color="sex", marginal="rug")
fig.show()


### Facets¶

ECDF Plots also support faceting

In [14]:
import plotly.express as px
df = px.data.tips()
fig = px.ecdf(df, x="total_bill", color="sex", facet_row="time", facet_col="day")
fig.show()

In [ ]:



Dash is an open-source framework for building analytical applications, with no Javascript required, and it is tightly integrated with the Plotly graphing library.

Learn about how to install Dash at https://dash.plot.ly/installation.

Everywhere in this page that you see fig.show(), you can display the same figure in a Dash application by passing it to the figure argument of the Graph component from the built-in dash_core_components package like this:

import plotly.graph_objects as go # or plotly.express as px
fig = go.Figure() # or any Plotly Express function e.g. px.bar(...)
# fig.update_layout( ... )

import dash
import dash_core_components as dcc
import dash_html_components as html

app = dash.Dash()
app.layout = html.Div([
dcc.Graph(figure=fig)
])