Distribution (pdf, cdf) of iris data

python

statistics

distribution

Author

kakamana

Published

January 6, 2023

Iris data set distribution (pdf and cdf) exploration

Lets explore distribution functions pdf and cdf using Iris data set

Code

import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
import warnings;
warnings.filterwarnings('ignore');

Code

iris=pd.read_csv('iris.csv')
iris.head()

	sepal_length	sepal_width	petal_length	petal_width	type
0	5.1	3.5	1.4	0.2	Iris-setosa
1	4.9	3.0	1.4	0.2	Iris-setosa
2	4.7	3.2	1.3	0.2	Iris-setosa
3	4.6	3.1	1.5	0.2	Iris-setosa
4	5.0	3.6	1.4	0.2	Iris-setosa

Code

iris.shape

(150, 5)

Code

iris.columns

Index(['sepal_length', 'sepal_width', 'petal_length', 'petal_width', 'type'], dtype='object')

Code

iris['type'].value_counts()

Iris-setosa        50
Iris-versicolor    50
Iris-virginica     50
Name: type, dtype: int64

Code

setosa=iris[iris['type']=="Iris-setosa"]
setosa['petal_length'].value_counts()

1.5    14
1.4    12
1.3     7
1.6     7
1.7     4
1.2     2
1.9     2
1.1     1
1.0     1
Name: petal_length, dtype: int64

Basic scatter plot

Code

iris.plot(kind='scatter',x='sepal_length',y='sepal_width');
plt.show()

Code

#here we plot the scatter diagram with colour coding
sns.set_style('whitegrid')
sns.FacetGrid(iris,hue="type",aspect = 2).map(plt.scatter,"sepal_length","sepal_width").add_legend()
plt.show()

Pair plotting

For cross-referencing

Code

plt.close()
sns.set_style("whitegrid")
sns.pairplot(iris,hue="type",size=3)
plt.show()

probability density function (pdf), cumulative distribution function (cdf) and histogram

Code

setosa=iris.loc[iris["type"]=="Iris-setosa"]
versicolor=iris.loc[iris["type"]=="Iris-versicolor"]
virginica=iris.loc[iris["type"]=="Iris-virginica"]

Code

plt.plot(setosa["petal_length"],np.zeros_like(setosa['petal_length']), 'o')
plt.plot(versicolor["petal_length"],np.zeros_like(versicolor['petal_length']), 'o')
plt.plot(virginica["petal_length"],np.zeros_like(virginica['petal_length']), 'o')
plt.show()

Code

sns.distplot(iris[iris['type']== 'Iris-setosa']['petal_length'])

<AxesSubplot:xlabel='petal_length', ylabel='Density'>

Code

sns.FacetGrid(iris, hue="type",aspect = 2).map(sns.distplot, "petal_length") \
   .add_legend();
plt.show();

Code

sns.FacetGrid(iris, hue="type", aspect = 2).map(sns.distplot, "petal_width") \
   .add_legend();
plt.show();

Code

sns.FacetGrid(iris, hue="type", aspect=2).map(sns.distplot, "sepal_length") \
   .add_legend();
plt.show();

Code

sns.FacetGrid(iris, hue="type", aspect=2).map(sns.distplot, "sepal_width") \
   .add_legend();
plt.show();

PDF point evaluation

Code

counts, bin_edges = np.histogram(setosa['petal_length'], bins=10,
                                 density = False)

print("histogram counts\n",counts)
pdf = counts/(sum(counts))
print("Sum of count is\n",sum(counts))
print("bin edges \n",bin_edges)
print("PDF below \n",pdf);

plt.gca().legend(('Pdf'))
plt.title('PDF and PDF For iris_setosa')
plt.xlabel("Petal length")
plt.ylabel("Percentage")
plt.plot(bin_edges[1:],pdf)

histogram counts
 [ 1  1  2  7 12 14  7  4  0  2]
Sum of count is
 50
bin edges 
 [1.   1.09 1.18 1.27 1.36 1.45 1.54 1.63 1.72 1.81 1.9 ]
PDF below 
 [0.02 0.02 0.04 0.14 0.24 0.28 0.14 0.08 0.   0.04]

[<matplotlib.lines.Line2D at 0x1a5ae102100>]

CDF point evaluation

Code

counts, bin_edges = np.histogram(setosa['petal_length'], bins=10,
                                 density = False)

print("histogram counts\n",counts)
pdf = counts/(sum(counts))
print("Sum of count is\n",sum(counts))
print("bin edges \n",bin_edges)
print("PDF is below  \n",pdf);

cdf = np.cumsum(pdf)
print("CDF is below\n",cdf)
plt.gca().legend(('Cdf'))
plt.title('CDF For iris_setosa')
plt.xlabel("Petal length")
plt.ylabel("Percentage")

plt.plot(bin_edges[1:],cdf)

histogram counts
 [ 1  1  2  7 12 14  7  4  0  2]
Sum of count is
 50
bin edges 
 [1.   1.09 1.18 1.27 1.36 1.45 1.54 1.63 1.72 1.81 1.9 ]
PDF is below  
 [0.02 0.02 0.04 0.14 0.24 0.28 0.14 0.08 0.   0.04]
CDF is below
 [0.02 0.04 0.08 0.22 0.46 0.74 0.88 0.96 0.96 1.  ]

[<matplotlib.lines.Line2D at 0x1a5ae1721c0>]

Code

counts, bin_edges = np.histogram(setosa['petal_length'], bins=10,
                                 density = True)

print(counts)
pdf = counts/(sum(counts))
print(pdf);
print(bin_edges)

#compute CDF
cdf = np.cumsum(pdf)
plt.plot(bin_edges[1:],pdf)
plt.plot(bin_edges[1:], cdf)
plt.gca().legend(('Pdf','Cdf'))
plt.title('PDF and CDF For iris_setosa')
plt.xlabel("Petal length")
plt.ylabel("Percentage")
plt.show();

[0.22222222 0.22222222 0.44444444 1.55555556 2.66666667 3.11111111
 1.55555556 0.88888889 0.         0.44444444]
[0.02 0.02 0.04 0.14 0.24 0.28 0.14 0.08 0.   0.04]
[1.   1.09 1.18 1.27 1.36 1.45 1.54 1.63 1.72 1.81 1.9 ]

Code

counts, bin_edges = np.histogram(setosa['petal_length'], bins=10,
                                 density = True)
pdf = counts/(sum(counts))
print(pdf);
print(bin_edges);
cdf = np.cumsum(pdf)
plt.plot(bin_edges[1:],pdf);
plt.plot(bin_edges[1:], cdf)


counts, bin_edges = np.histogram(setosa['petal_length'], bins=20,
                                 density = True)
pdf = counts/(sum(counts))
plt.plot(bin_edges[1:],pdf);
plt.gca().legend(('Pdf','Cdf','bin edges'))
plt.title('PDF and CDF For iris_setosa')
plt.xlabel("Petal length")
plt.ylabel("Percentage")
plt.show();

[0.02 0.02 0.04 0.14 0.24 0.28 0.14 0.08 0.   0.04]
[1.   1.09 1.18 1.27 1.36 1.45 1.54 1.63 1.72 1.81 1.9 ]

All type of petals/species PDF & CDF

Code

counts, bin_edges = np.histogram(setosa['petal_length'], bins=10,
                                 density = True)
pdf = counts/(sum(counts))
print(pdf);
print(bin_edges)
cdf = np.cumsum(pdf)
plt.plot(bin_edges[1:],pdf)
plt.plot(bin_edges[1:], cdf)


# virginica
counts, bin_edges = np.histogram(virginica['petal_length'], bins=10,
                                 density = True)
pdf = counts/(sum(counts))
print(pdf);
print(bin_edges)
cdf = np.cumsum(pdf)
plt.plot(bin_edges[1:],pdf)
plt.plot(bin_edges[1:], cdf)


#versicolor
counts, bin_edges = np.histogram(versicolor['petal_length'], bins=10,
                                 density = True)
pdf = counts/(sum(counts))
print(pdf);
print(bin_edges)
cdf = np.cumsum(pdf)
plt.plot(bin_edges[1:],pdf)
plt.plot(bin_edges[1:], cdf)

plt.title('PDF and CDF For iris_versicolor')
plt.xlabel("Petal length")
plt.ylabel("Percentage")

plt.show();

[0.02 0.02 0.04 0.14 0.24 0.28 0.14 0.08 0.   0.04]
[1.   1.09 1.18 1.27 1.36 1.45 1.54 1.63 1.72 1.81 1.9 ]
[0.02 0.1  0.24 0.08 0.18 0.16 0.1  0.04 0.02 0.06]
[4.5  4.74 4.98 5.22 5.46 5.7  5.94 6.18 6.42 6.66 6.9 ]
[0.02 0.04 0.06 0.04 0.16 0.14 0.12 0.2  0.14 0.08]
[3.   3.21 3.42 3.63 3.84 4.05 4.26 4.47 4.68 4.89 5.1 ]

Calculation of mean, variance & std. deviation

Code

#Mean, Variance, Std-deviation,
print("Means:")
print(np.mean(setosa["petal_length"]))
#Mean with an outlier.
print(np.mean(np.append(setosa["petal_length"],50)));
print(np.mean(virginica["petal_length"]))
print(np.mean(versicolor["petal_length"]))

print("\nStd-dev:");
print(np.std(setosa["petal_length"]))
print(np.std(virginica["petal_length"]))
print(np.std(versicolor["petal_length"]))

Means:
1.464
2.4156862745098038
5.5520000000000005
4.26

Std-dev:
0.17176728442867112
0.546347874526844
0.4651881339845203

Median, quantiles, percentiles & IQRs

Code

#Median, Quantiles, Percentiles, IQR.
print("\nMedians:")
print(np.median(setosa["petal_length"]))
#Median with an outlier
print(np.median(np.append(setosa["petal_length"],50)));
print(np.median(virginica["petal_length"]))
print(np.median(versicolor["petal_length"]))


print("\nQuantiles:")
print(np.percentile(setosa["petal_length"],np.arange(0, 100, 25)))
print(np.percentile(virginica["petal_length"],np.arange(0, 100, 25)))
print(np.percentile(versicolor["petal_length"], np.arange(0, 100, 25)))

print("\n90th Percentiles:")
print(np.percentile(setosa["petal_length"],90))
print(np.percentile(virginica["petal_length"],90))
print(np.percentile(versicolor["petal_length"], 90))

from statsmodels import robust
print ("\nMedian Absolute Deviation")
print(robust.mad(setosa["petal_length"]))
print(robust.mad(virginica["petal_length"]))
print(robust.mad(versicolor["petal_length"]))


Medians:
1.5
1.5
5.55
4.35

Quantiles:
[1.    1.4   1.5   1.575]
[4.5   5.1   5.55  5.875]
[3.   4.   4.35 4.6 ]

90th Percentiles:
1.7
6.31
4.8

Median Absolute Deviation
0.14826022185056031
0.6671709983275211
0.5189107764769602

Boxploting

Code

sns.boxplot(x='type',y='petal_length', data=iris)
plt.show()

Violiin plotting

Code

sns.violinplot(x="type", y="petal_length", data=iris, size=8)
plt.show()

Lastly multivariate probability density & contour plot

Code

sns.jointplot(x="petal_length", y="petal_width", data=setosa, kind="kde");
plt.show();