Quantile bucketing is a feature transformation method that divides values into buckets containing approximately equal numbers of examples. Because the buckets are based on distribution rather than equal numeric width, different buckets may cover different value ranges.
Distributing a feature's values into buckets so that each bucket contains the same (or almost the same) number of examples. For example, the following figure divides 44 points into 4 buckets, each of which contains 11 points. In order for each bucket in the figure to contain the same number of points, some buckets span a different width of x-values. !44 data points divided into 4 buckets of 11 points each. Although each bucket contains the same number of data points, some buckets contain a wider range of feature values than other buckets. See Numerical data: Binning in Machine Learning Crash Course for more information.