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Plotting a Gamma distribution in Python is a relatively simple process. It involves importing the necessary libraries, such as SciPy, NumPy and Matplotlib, defining the parameters of the Gamma distribution (shape, scale) and using the SciPy library to generate the random samples and plot them using the Matplotlib library. The plot can then be customized to show the probability density of the Gamma distribution. Finally, the plot can be saved as an image file or displayed directly on the screen. Examples of plotting a Gamma distribution in Python are provided to demonstrate the process.
In statistics, the Gamma distribution is often used to model probabilities related to waiting times.
The following examples show how to use the function to plot one or more Gamma distributions in Python.
Example 1: Plot One Gamma Distribution
The following code shows how to plot a Gamma distribution with a shape parameter of 5 and a scale parameter of 3 in Python:
import numpy as np import scipy.stats as stats import matplotlib.pyplot as plt #define x-axis values x = np.linspace (0, 40, 100) #calculate pdf of Gamma distribution for each x-value y = stats.gamma.pdf(x, a=5, scale=3) #create plot of Gamma distribution plt.plot(x, y) #display plot plt.show()
The x-axis displays the potential values that a Gamma distributed random variable can take on and the y-axis shows the corresponding PDF values of the Gamma distribution with a shape parameter of 5 and scale parameter of 3.
Example 2: Plot Multiple Gamma Distributions
The following code shows how to plot multiple Gamma distributions with various shape and scale parameters:
import numpy as np import scipy.stats as stats import matplotlib.pyplot as plt #define three Gamma distributions x = np.linspace(0, 40, 100) y1 = stats.gamma.pdf(x, a=5, scale=3) y2 = stats.gamma.pdf(x, a=2, scale=5) y3 = stats.gamma.pdf(x, a=4, scale=2) #add lines for each distribution plt.plot(x, y1, label=shape=5, scale=3') plt.plot(x, y2, label='shape=2, scale=5') plt.plot(x, y3, label='shape=4, scale=2') #add legend plt.legend() #display plot plt.show()
Notice that the shape of the Gamma distribution can vary quite a bit depending on the shape and scale parameters.
Related:
The following tutorials explain how to plot other common distributions in Python: