QQ, also known as Tencent QQ, is an instant messaging software platform that plays a vital role in China's social networking scene. With over 700 million daily active users, QQ is primarily used for online messaging, casual video and voice calls, document-sharing, and social networking.
What are Q-Q Plots?
In statistics, Q-Q (quantile-quantile) plots play a crucial role in graphically analyzing and comparing two probability distributions by plotting their quantiles against each other. If the two distributions being compared are exactly equal, then the points on the Q-Q plot will perfectly lie on a straight line y = x.
How Does a Q-Q Plot Work?
To create a Q-Q plot, we plot theoretical quantiles (standard normal variate) on the x-axis and the ordered values of the random variable on the y-axis. This forms a beautiful and smooth straight-line-like structure from each point plotted on the graph. If all the points fall perfectly on a straight line, then we can conclude that the distribution is normally distributed.
What are Skewed Q-Q Plots?
Q-Q plots are also used to find the skewness (a measure of asymmetry) of a distribution. A skewed Q-Q plot deviates from the straight line at one end, indicating whether the distribution has a longer tail on the left (negatively skewed) or right (positively skewed).
What are Tailed Q-Q Plots?
Similarly, we can talk about the kurtosis (a measure of "tailedness") of the distribution by simply looking at its Q-Q plot. A fat-tailed distribution will have both ends deviate from the straight line, while a thin-tailed distribution will form a Q-Q plot with negligible deviation at the ends.
How Much Data Do We Need for a Q-Q Plot?
Note that when the data points are few, the Q-Q plot does not perform very precisely, and it fails to give a conclusive answer. When we have an ample amount of data points and plot a Q-Q plot using a large data set, however, then it gives a result significant enough to draw clears about the type of distribution.
Q-Q Plots Implementation Examples in Python
Here are simple implementations of plotting a Q-Q plot in Python using various libraries:
- Using Statsmodels:
sm.qqplot(data_points, line ='45') - Using Scipy:
stats.probplot(z, dist="norm", plot=plt)
These examples demonstrate how to create and interpret Q-Q plots using Python.
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