Python - Skew-Normal Distribution in Statistics

Python - Skew-Normal Distribution in Statistics

The skew-normal distribution is a generalization of the normal (Gaussian) distribution that introduces skewness. While the normal distribution is symmetric, the skew-normal distribution can be asymmetric based on a shape parameter which controls the direction and degree of skewness.

The probability density function (PDF) of the skew-normal distribution is given by:

f(x;ξ,ω,α)=2ϕ(z)Φ(αz)

Where:

  • ϕ is the standard normal density function.
  • Φ is the standard normal cumulative distribution function (CDF).
  • z=(x−ξ)/ω.
  • ξ is the location parameter.
  • ω is the scale parameter.
  • α is the shape parameter. When α=0, the distribution is a standard normal.

In Python, the scipy.stats module provides the skewnorm class which represents the skew-normal distribution.

Here's how to use it:

1. Install the required library:

If you don't have scipy installed, install it using pip:

pip install scipy

2. Using the skew-normal distribution in Python:

import numpy as np import matplotlib.pyplot as plt from scipy.stats import skewnorm # Parameters for the skew-normal distribution a = 4 # Shape parameter (degree and direction of skewness) loc = 0 # Location parameter (analogous to the mean of the normal distribution) scale = 1 # Scale parameter (analogous to the standard deviation of the normal distribution) # Generating some data x = np.linspace(-3, 3, 1000) pdf_values = skewnorm.pdf(x, a, loc, scale) # Plotting the PDF of the skew-normal distribution plt.plot(x, pdf_values, label=f'Skew={a}') plt.title('Skew-Normal Distribution') plt.xlabel('x') plt.ylabel('PDF') plt.legend() plt.grid(True) plt.show()

This code will plot the probability density function (PDF) of a skew-normal distribution with the given parameters.

You can also use other methods provided by skewnorm such as:

  • skewnorm.cdf(): To get the cumulative distribution function (CDF).
  • skewnorm.rvs(): To generate random variables.
  • skewnorm.mean(), skewnorm.var(), etc.: To get properties like mean and variance.

Adjust the shape parameter a to see how the distribution changes. Positive values of a produce right-skewed distributions, while negative values produce left-skewed distributions.

More Tags

classification ads synchronization amazon-ecs facebook-login dart-2 angular-material regex-greedy decimalformat pow

More Programming Guides

Other Guides

More Programming Examples