In Python, you can utilize the scipy.stats module to calculate the quantiles of a dataset and compare them with the quantiles of a desired distribution. Here's a general approach to achieve this:
Import the necessary libraries:
import numpy as np
import scipy.stats as stats
import matplotlib.pyplot as plt
Generate or obtain your dataset of measurements:
# Example dataset of measurements
data = np.random.normal(loc=0, scale=1, size=1000)
Calculate the quantiles of the dataset:
quantiles_data = np.linspace(0, 1, num=100) # Quantiles range from 0 to 1
data_quantiles = np.quantile(data, quantiles_data)
Define the desired distribution and calculate its quantiles:
# Example: Normal distribution
distribution = stats.norm(loc=0, scale=1)
distribution_quantiles = distribution.ppf(quantiles_data)
Plot the quantiles:
plt.scatter(distribution_quantiles, data_quantiles)
plt.plot([np.min(distribution_quantiles), np.max(distribution_quantiles)],
[np.min(distribution_quantiles), np.max(distribution_quantiles)],
color='red', linestyle='--')
plt.xlabel('Quantiles of Desired Distribution')
plt.ylabel('Quantiles of Data')
plt.title('Quantile-Quantile Plot')
plt.show()
This code generates a scatter plot where the x-axis represents the quantiles of the desired distribution, and the y-axis represents the quantiles of the dataset. The red dashed line represents the ideal relationship where the quantiles of the data perfectly align with the quantiles of the desired distribution.
By observing the plot, you can assess whether the distribution of your measurements follows the expected distribution or deviates from it.