ENH: Option to return -inf/inf as lower/upper bound of quantiles, see…

doc/source/whatsnew/v0.24.0.txt

@@ -17,6 +17,9 @@ New features
 
 - ``ExcelWriter`` now accepts ``mode`` as a keyword argument, enabling append to existing workbooks when using the ``openpyxl`` engine (:issue:`3441`)
 
+- :func: quantile and :func: qcut now accept ``bounded`` as a keyword
+  argument, allowing for unbounded quantiles such that the lower/upper bounds are -inf/inf (:issue:`17282`)
+
 .. _whatsnew_0240.enhancements.extension_array_operators:
 
 ``ExtensionArray`` operator support

pandas/core/algorithms.py

@@ -985,7 +985,7 @@ def _broadcast(arr_or_scalar, shape):
 }
 
 
-def quantile(x, q, interpolation_method='fraction'):
+def quantile(x, q, bounded=True, interpolation_method='fraction'):
     """
     Compute sample quantile or quantiles of the input array. For example, q=0.5
     computes the median.
@@ -1002,6 +1002,9 @@ def quantile(x, q, interpolation_method='fraction'):
         Values from which to extract score.
     q : scalar or array
         Percentile at which to extract score.
+    bounded : bool, optional
+        Whether to use the min/max of the distribution as the lower/upper
+        bounds or use -inf/inf.
     interpolation_method : {'fraction', 'lower', 'higher'}, optional
         This optional parameter specifies the interpolation method to use,
         when the desired quantile lies between two data points `i` and `j`:
@@ -1038,6 +1041,12 @@ def _interpolate(a, b, fraction):
         return a + (b - a) * fraction
 
     def _get_score(at):
+        if not bounded:
+            if at == 0:
+                return -np.inf
+            elif at == 1:
+                return np.inf
+
         if len(values) == 0:
             return np.nan
 

pandas/core/reshape/tile.py

@@ -238,7 +238,8 @@ def cut(x, bins, right=True, labels=None, retbins=False, precision=3,
                                 series_index, name, dtype)
 
 
-def qcut(x, q, labels=None, retbins=False, precision=3, duplicates='raise'):
+def qcut(x, q, labels=None, retbins=False, precision=3, bounded=True, 
+         duplicates='raise'):
     """
     Quantile-based discretization function. Discretize variable into
     equal-sized buckets based on rank or based on sample quantiles. For example
@@ -260,6 +261,9 @@ def qcut(x, q, labels=None, retbins=False, precision=3, duplicates='raise'):
         is given as a scalar.
     precision : int, optional
         The precision at which to store and display the bins labels
+    bounded : bool, optional
+        Whether to use the min/max of the distribution as the lower/upper
+        bounds or use -inf/inf.
     duplicates : {default 'raise', 'drop'}, optional
         If bin edges are not unique, raise ValueError or drop non-uniques.
 
@@ -301,7 +305,7 @@ def qcut(x, q, labels=None, retbins=False, precision=3, duplicates='raise'):
         quantiles = np.linspace(0, 1, q + 1)
     else:
         quantiles = q
-    bins = algos.quantile(x, quantiles)
+    bins = algos.quantile(x, quantiles, bounded=bounded)
     fac, bins = _bins_to_cuts(x, bins, labels=labels,
                               precision=precision, include_lowest=True,
                               dtype=dtype, duplicates=duplicates)