Python Scipy Stats Skew [With 8 Examples]

In this Python tutorial, we will learn about the “Python Scipy Skew” where we will learn about skewness which is a metric for the asymmetry of a real-valued random variable’s probability distribution concerning its mean using Python Scipy. And additionally, we will also cover the following topics.

  • Python Scipy Stats Skew
  • Python Scipy Stats Skewnorm
  • Python Scipy Stats Skew t
  • Python Scipy Stats Skew distribution
  • Python Scipy Stats Skew Logcdf
  • Python Scipy Stats Skew axis
  • Python Scipy Stats Skew CDF
  • Python Scipy Stats Skew Logpdf

What is skew?

A deviation from a set of data’s normal distribution or symmetrical bell curve is referred to as skewness. The term “skewed” refers to a curve that has been moved to the left or right. The degree to which a particular distribution deviates from the normal distribution can be expressed quantitatively as skewness.

Varying degrees of right (positive) or left (negative) skewness can be seen in distributions. Zero skewness is shown via a normal distribution (bell curve).

For both positive and negative skews, the “tail” or collection of data points far from the median is affected. Positive skew describes a longer or fatter tail on the right side of the distribution, whereas negative skew describes a longer or fatter tail on the left side of the distribution. These two skews describe the weight or direction of the distribution.

Positively skewed data will have a mean that is higher than the median. The mean of negatively skewed data will be less than the median, which is the exact reverse of what happens in a positively skewed distribution. No matter how long or fat the tails are, the distribution exhibits zero skewness if the data is graphed symmetrically.

Read: Python Scipy Eigenvalues

Scipy Stats Skew

The Python Scipy module scipy.stats has a method skew() that calculate a data set’s sample skewness.

The skewness for data that is regularly distributed should be close to zero. If the skewness value for a continuous unimodal distribution is greater than zero, the right tail of the distribution will be given more weight. To check whether the skewness value is statistically close enough to zero, use the skewtest function.

The syntax is given below.

scipy.stats.skew(a, axis=1, bias=False, nan_policy='throw')

Where parameters are:

  • a(array_data): n-dimensional array from which to determine the mode (s).
  • bias(boolean): If this is untrue, statistical bias is removed from the calculations.
  • nan_plociy(): Specifies what to do in cases when the input contains nan. (‘Propagate’ is the default) The following choices are available:
  1. propagate: nan is returned
  2. raise: throws a mistake
  3. omit: ignoring nan values.
  • axis(int): The direction of the axis. The default is 0. Consider the entire array an if None.

The method skew() returns skewness(when all values are equal, the skewness of data along an axis returns 0) of type ndarray.

Let’s take an example by passing the array to the method skew() using the below python code.

from scipy import stats
stats.skew([2,5,3,7,8,9,4])
Scipy Stats Skew
Scipy Stats Skew

This is how to compute the skewness of the given array of data using the method skew() of Python Scipy.

Read: Python Scipy Freqz

Python Scipy Stats Skewnorm

The Python Scipy has a skew-normal continuous random variable or object skewnorm() in a module scipy.stats. From it, the skewnorm object inherits a set of general methods, which it completes with information unique to this distribution.

A real number is accepted by skewnorm as the skewness parameter. The distribution resembles a normal distribution when a = 0. The loc and scale parameters can be used to scale or shift the distribution.

The syntax is given below.

scipy.stats.skewnorm.method_name(x,q,loc,scale,size,moments)

Where parameters are:

  • x: Higher and lower tail probabilities.
  • q: For spcifiying the quantiles.
  • loc: It is used to specify the mean, by default it is 0.
  • moments: It is used to calculate statistics like standard deviation, kurtosis, and mean.
  • scale: It is used to specify the standard deviation, by default it is 1.

Let’s take an example by following the below steps:

Import the required libraries using the below code.

import numpy as np
import matplotlib.pyplot as plt
from scipy import stats

Create observation data values and calculate the probability density function from these data values with mean = 0 and standard deviation = 1.

a = 3
observatin_x = np.linspace(-4,4,200)
pdf_skewnorm = stats.skewnorm.pdf(observatin_x,a,loc=0,scale=1)

Plot the created distribution using the below code.

plt.plot(observatin_x,pdf_skewnorm)
plt.xlabel('x-values')
plt.ylabel('pdf_norm_values')
plt.title("Skewnorm Probability density function")
plt.show()
Python Scipy Stats Skewnorm
Python Scipy Stats Skewnorm

Read: Python Scipy Minimize

Python Scipy Stats Skew axis

The Python Scipy skew() accepts parameter axis for computing the skew along the specific axis that we have learned above subsection “Python Scipy Stats Skew”.

A two-dimensional array has two corresponding axes, one running horizontally across columns (axis 1) and the other vertically across rows (axis 0).

Let’s take an example and compute the skew of the array based on axes by following the below steps:

Import the required libraries using the below python code.

from scipy.stats import skew
import numpy as np

Create a 2d array and compute the skew using the below code.

array=np.array([[5, 4, 9, 8, 2],
                [3, 6, 8, 5, 7],
                [7, 5, 8, 3, 6]])
skew(array)

In the above code, the skew is computed on the whole array, now specify the axis = 1 using the below code.

skew(array, axis = 1)
Python Scipy Stats Skew axis
Python Scipy Stats Skew axis

Look at the above output, we have computed the skew on the whole array or along the horizontal axis.

Read: Python Scipy Exponential – Helpful Tutorial

Python Scipy Stats Skew distribution

There are two types of distributions, left-skewed, and right-skewed.

  • A distribution that is left-skewing has a lengthy left tail. Distributions that are negatively skewed are also known as left-skewed distributions. This is due to the number line having a significant negative tail. Additionally, the peak is to the left of the mean.
  • There is a long right tail in a right-skewed distribution. Positive-skew distributions, or right-skewed distributions, are another name for them. This is due to the number line having a long tail in the positive direction. Additionally, the mean is to the right of the peak.

So here in this section, we will build both skew distributions that we have learned above.

Import the required libraries using the below python code.

import pylab as p
from scipy.stats import skew
import numpy as np 

Generate x and y data using the below code.

x_data = np.linspace(8, -15, 500 )
y_data = 1./(np.sqrt(2.*np.pi)) * np.exp( -.2*(x1)**2  )

Compute and plot the left skew using the below code.

p.plot(x_data, y_data, '.')
  
print( '\n Left Skewness for data : ', skew(y_data))
Python Scipy Stats Skew distribution example
Python Scipy Stats Skew distribution example

Again compute and plot the right skew using the below code.

x_data = np.linspace(-8, 15, 500 )
y_data = 1./(np.sqrt(2.*np.pi)) * np.exp( -.2*(x_data)**2  )
  
p.plot(x_data, y_data, '.')
  
print( '\n Left Skewness for data : ', skew(y_data))
Python Scipy Stats Skew distribution
Python Scipy Stats Skew distribution

This is how to compute the left and right skew using the method skew() of Python Scipy.

Read: Python Scipy Chi-Square Test

Python Scipy Stats Skew Logcdf

The object skewnorm() has method logcdf() that computes the log of the cumulative distribution of skew norm.

The syntax is given below code.

scipy.stats.skewnorm.logcdf(x,a,loc,scale)

Where parameters are:

x: Higher and lower tail probabilities.
a: It is a skewness parameter.
loc: It is used to specify the mean, by default it is 0.
scale: It is used to specify the standard deviation, by default it is 1.

Let’s do an example by following the below steps:

Import the required libraries using the below code.

import numpy as np
import matplotlib.pyplot as plt
from scipy import stats

Create observation data values and calculate the log of cumulative distribution from these data values with mean = 0 and standard deviation = 1.

a = 1
observatin_x = np.linspace(-5,5,300)
logcdf_skewnorm = stats.skewnorm.logcdf(observatin_x,a,loc=0,scale=1)

Plot the created distribution using the below code.

plt.plot(observatin_x,logcdf_skewnorm)
plt.xlabel('x-values')
plt.ylabel('logcdf_norm_values')
plt.title("Skewnorm log of Cumulative distribution function")
plt.show()

Python Scipy Stats Skew Norm CDF

We have already covered about the skewnorm() Python Scipy in the above subsection ” Python Scipy Stats Skewnorm”, the object skewnorm() has method CDF() that computes the cumulative distribution of skew norm.

The syntax is given below code.

scipy.stats.skewnorm.cdf(x,a,loc,scale)

Where parameters are:

x: Higher and lower tail probabilities.
a: It is a skewness parameter.
loc: It is used to specify the mean, by default it is 0.
scale: It is used to specify the standard deviation, by default it is 1.

Let’s do an example by following the below steps:

Import the required libraries using the below code.

import numpy as np
import matplotlib.pyplot as plt
from scipy import stats

Create observation data values and calculate the cumulative distribution from these data values with mean = 0 and standard deviation = 1.

a = 2
observatin_x = np.linspace(-5,5,300)
cdf_skewnorm = stats.skewnorm.cdf(observatin_x,a,loc=0,scale=1)

Plot the created distribution using the below code.

plt.plot(observatin_x,cdf_skewnorm)
plt.xlabel('x-values')
plt.ylabel('cdf_norm_values')
plt.title("Skewnorm Cumulative distribution function")
plt.show()
Python Scipy Stats Skew Norm CDF
Python Scipy Stats Skew Norm CDF

This is how to compute the CDF of skew using the method skewnorm.cdf() of Python Scipy.

Read: Python Scipy Special Module

Python Scipy Stats Skew Logpdf

The object skewnorm() of Python Scipy has a method logpdf() that computes the log of the probability density of the skew norm.

The syntax is given below code.

scipy.stats.skewnorm.logpdf(x,a,loc,scale)

Where parameters are:

x: Higher and lower tail probabilities.
a: It is a skewness parameter.
loc: It is used to specify the mean, by default it is 0.
scale: It is used to specify the standard deviation, by default it is 1.

Let’s do an example by following the below steps:

Import the required libraries using the below code.

import numpy as np
import matplotlib.pyplot as plt
from scipy import stats

Create observation data values and calculate the log of probability density from these data values with mean = 0 and standard deviation = 1.

a = 5
observatin_x = np.linspace(-3,3,400)
logpdf_skewnorm = stats.skewnorm.logpdf(observatin_x,a,loc=0,scale=1)

Plot the created distribution using the below code.

plt.plot(observatin_x,logpdf_skewnorm)
plt.xlabel('x-values')
plt.ylabel('logpdf_norm_values')
plt.title("Skewnorm Log of the probability density function")
plt.show()
Python Scipy Stats Skew Logpdf
Python Scipy Stats Skew Logpdf

Read: Scipy Linalg – Helpful Guide

Python Scipy Stats Skew t

Here in this section, we will generate the student t sample using the method t.rvs() of Python Scipy Stats, then we will pass this data to the method skew() of Python Scipy to compute the skew of this data.

Let’s understand with an example by following the below steps:

Import the required libraries using the below python code.

from scipy.stats import t, skew

Generate the random numbers or samples from student t distribution using the below code.

degree_of_freedom = 2.74
r = t.rvs(degree_of_freedom, size=1000)

Now compute the skew of the above-generated sample using the below code.

skew(r)
Python Scipy Stats Skew t
Python Scipy Stats Skew t

The skew of the student t sample is 0.381, as we can see in the above output.

This is how to compute the skew of the student t sample using the method skew() of Python Scipy.

Also, take a look at some more Python SciPy tutorials.

So, in this Python tutorial, we understood the use of Python Scipy Stats Skew with multiple examples. And we have also covered the following topics in this tutorial.

  • Python Scipy Stats Skew
  • Python Scipy Stats Skewnorm
  • Python Scipy Stats Skew t
  • Python Scipy Stats Skew distribution
  • Python Scipy Stats Skew Logcdf
  • Python Scipy Stats Skew axis
  • Python Scipy Stats Skew CDF
  • Python Scipy Stats Skew Logpdf