QQ (Quantile-Quantile) Plot in Python

Introduction:

Python offers a QQ plot, a graphical tool for comparing a dataset's distribution with a known theoretical one, enabling the determination of dataset in following a certain probability distribution.

What is a Quantile-Quantile Plot?

A quantile-quantile plot (or QQ plot) is a graphical tool used to compare the distributions of two datasets. By plotting their quantiles against each other, a QQ plot helps you visually assess whether the two datasets come from similar distributions. If the points on the plot form a straight line, it suggests that the distributions are similar. If they deviate from a straight line, it indicates differences between the distributions.

Let us now look at the interpretations of the QQ plot:

Interpretations

• Every quantile point is located on a straight line, or very near one, at a 45-degree angle to the x-axis. The distributions of the two samples are comparable.
  
  Furthermore, obtaining a perfectly straight line in practice is never feasible; instead, the plot appears as follows. The points in this instance are almost exactly on a straight line.
  
• The y-quantiles are lower than the x-quantiles. This suggests that y values often tend to be lower than x values.
  
  The plot shows that obtaining 100% accuracy is not always possible, with some points above the line and most points below it. As a result, we may state that the distributions differ.
  
• The x-quantiles are less than the y-quantiles. Therefore, it means that the x-values are, on average, less than the values of the y.
  
  It also implies that up to a breaking point, the y-quantiles are smaller than the x-quantiles. After that point, the y-quantiles are higher than the x-quantiles.
  

Implementation of QQ plot in Python

We will now look at the following example demonstrating the making of the QQ (Quantile-Quantile) plot in Python with the help of the statsmodel module:

Example:

Output:

Explanation:

This Python script creates a QQ plot, a graphical tool for comparing a sample's distribution to a given probability distribution, using NumPy and Statsmodels. It creates 200 random data points (np.random.normal(0, 1, 200)) that are sampled from a conventional normal distribution and displays them against the normal distribution's anticipated quantiles. The QQ plot is made using the sm. qqplot() method, and it is shown using py.show().

Conclusion:

To sum up, the Quantile-Quantile (QQ) plot is an effective visual aid that evaluates the degree to which the distribution of a sample resembles a theoretical distribution, like the normal distribution. You may rapidly determine whether two distributions are similar or different by comparing quantiles from the sample distribution versus quantiles from the reference distribution. QQ plots offer a clear, graphical representation of these comparisons, as the Python example shows, and can assist you in making well-informed judgements regarding statistical analysis and data distribution.