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Discrete Frequency in Python

Learn how to perform discrete frequency analysis using Python.

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Imports

The tutorial below imports Numpy, Pandas, and SciPy.

In [1]:
import plotly.plotly as py
import plotly.graph_objs as go
from plotly.tools import FigureFactory as FF

import numpy as np
import pandas as pd
import scipy

Import Data

We will import a dataset to perform our discrete frequency analysis on. We will look at the consumption of alcohol by country in 2010.

In [2]:
data = pd.read_csv('https://raw.githubusercontent.com/plotly/datasets/master/2010_alcohol_consumption_by_country.csv')
df = data[0:10]

table = FF.create_table(df)
py.iplot(table, filename='alcohol-data-sample')
Out[2]:

Probability Distribution

We can produce a histogram plot of the data with the y-axis representing the probability distribution of the data.

In [3]:
x = data['alcohol'].values.tolist()

trace = go.Histogram(x=x, histnorm='probability',
                     xbins=dict(start=np.min(x),
                                size=0.25,
                                end=np.max(x)),
                     marker=dict(color='rgb(25, 25, 100)'))

layout = go.Layout(
    title="Histogram with Probability Distribution"
)

fig = go.Figure(data=go.Data([trace]), layout=layout)
py.iplot(fig, filename='histogram-prob-dist')
Out[3]:

Frequency Counts

In [4]:
trace = go.Histogram(x=x,
                     xbins=dict(start=np.min(x),
                                size=0.25,
                                end=np.max(x)),
                     marker=dict(color='rgb(25, 25, 100)'))

layout = go.Layout(
    title="Histogram with Frequency Count"
)

fig = go.Figure(data=go.Data([trace]), layout=layout)
py.iplot(fig, filename='histogram-discrete-freq-count')
Out[4]:

Percentage

In [5]:
trace = go.Histogram(x=x, histnorm='percent',
                     xbins=dict(start=np.min(x),
                                size=0.25,
                                end=np.max(x)),
                     marker=dict(color='rgb(50, 50, 125)'))

layout = go.Layout(
    title="Histogram with Frequency Count"
)

fig = go.Figure(data=go.Data([trace]), layout=layout)
py.iplot(fig, filename='histogram-percentage')
Out[5]:

Cumulative Density Function

We can also take the cumulatve sum of our dataset and then plot the cumulative density function, or CDF, as a scatter plot

In [6]:
cumsum = np.cumsum(x)

trace = go.Scatter(x=[i for i in range(len(cumsum))], y=10*cumsum/np.linalg.norm(cumsum),
                     marker=dict(color='rgb(150, 25, 120)'))
layout = go.Layout(
    title="Cumulative Distribution Function"
)

fig = go.Figure(data=go.Data([trace]), layout=layout)
py.iplot(fig, filename='cdf-dataset')
Out[6]:
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