QQ Plot

A QQ plot (quantile-quantile plot) is a graphical tool used to assess if a given data distribution approximately follows a specific theoretical distribution.

To construct a QQ plot, the quantiles of the observed data are plotted against the quantiles of a reference distribution (usually a theoretical distribution with known parameters).

If the points in a QQ plot fall on or approximately follow a straight line, it suggests that the data follows the chosen theoretical distribution.

If the points in a QQ plot deviate from a straight line, it indicates that the data does not conform to the chosen theoretical distribution.

By comparing the observed data quantiles against the quantiles of a normal distribution in a QQ plot, one can visually assess if the data follows a normal distribution.

Outliers or extreme values can be identified if they appear as points that significantly deviate from the expected straight line pattern in a QQ plot.

Some common features to interpret in a QQ plot are skewness, heavy tails, multimodality, or any departures from the straight line pattern.

A QQ plot has limitations in detecting certain types of departures from the theoretical distribution, as well as its dependence on the chosen reference distribution.

A QQ plot can still be used for small sample sizes, but its interpretation becomes less reliable due to increased randomness and uncertainty in quantile estimation.

Yes, other methods like Kolmogorov-Smirnov test, Anderson-Darling test, or graphical techniques like histograms can also be used to assess distributional fit.