Generalized Gamma Distribution in Python

Understanding Generalized Gamma Distribution

The generalized gamma distribution is a flexible probability distribution that extends the gamma and Weibull distributions. It is defined by three parameters: a shape parameter, another shape parameter, and a scale parameter. Python’s scipy library provides a function to generate and analyze this distribution.

Generating and Plotting Generalized Gamma Distribution

Step-by-Step Explanation with Code:

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

Import NumPy for numerical operations, Matplotlib for plotting, and the necessary function from SciPy.

a, c = 2.0, 3.0

Define shape parameters that control the shape of the distribution.

x = np.linspace(0, 5, 100)

Generate 100 evenly spaced values between 0 and 5 to serve as the x-axis.

pdf_values = gengamma.pdf(x, a, c)

Compute the probability density function values for the given x values.

plt.plot(x, pdf_values, label=f'Generalized Gamma (a={a}, c={c})')

Plot the probability density function with a label indicating the parameters used.

plt.xlabel('x')
plt.ylabel('Probability Density')
plt.title('Generalized Gamma Distribution')
plt.legend()
plt.grid(True)
plt.show()

Label the axes, add a title, enable the grid, and display the plot.

complete code:

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

a, c = 2.0, 3.0
x = np.linspace(0, 5, 100)
pdf_values = gengamma.pdf(x, a, c)

plt.plot(x, pdf_values, label=f'Generalized Gamma (a={a}, c={c})')
plt.xlabel('x')
plt.ylabel('Probability Density')
plt.title('Generalized Gamma Distribution')
plt.legend()
plt.grid(True)
plt.show()

Expected Output

A probability density function (PDF) plot for the Generalized Gamma distribution with a=2.0 and c=3.0.

Graph Output

A smooth curve representing the distribution. The shape of the curve depends on the parameters a and c.

• The x-axis represents the range of values.
• The y-axis represents the probability density.
• The curve rises, peaks, and then declines, showcasing the probability distribution.