class_docstr: Distribution class for the Incremental (Spline) Quantile Function in the
  paper ``Learning Quantile Functions without Quantile Crossing for
  Distribution-free Time Series Forecasting``
  by Park, Robinson, Aubet, Kan, Gasthaus, Wang
  
  Parameters
  ----------
  spline_knots, spline_heights
      Tensor parametrizing the x-positions (y-positions) of the spline knots
      Shape: (*batch_shape, (num_qk-1), num_pieces)
  qk_x, qk_y
      Tensor containing the increasing x-positions (y-positions) of the
      quantile knots, Shape: (*batch_shape, num_qk)
  beta_l, beta_r
      Tensor containing the non-negative learnable parameter of the
      left (right) tail, Shape: (*batch_shape,)
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docstr: Evaluates the tail functions at the quantile levels contained in alpha
  Parameters
  ----------
  alpha
      Input quantile levels
  axis
      Axis along which to expand
      For details of input_alpha shape and axis,
      refer to the description in quantile_internal
  left_tail
      If True, compute the quantile for the left tail
      Otherwise, compute the quantile for the right tail
  Returns
  -------
  Tensor
      Quantiles tensor, of the same shape as alpha
code: def quantile_tail(
      self,
      alpha: Tensor,
      axis: Optional[int] = None,
      left_tail: bool = True,
  ) -> Tensor:
      r"""
      Evaluates the tail functions at the quantile levels contained in alpha
      Parameters
      ----------
      alpha
          Input quantile levels
      axis
          Axis along which to expand
          For details of input_alpha shape and axis,
          refer to the description in quantile_internal
      left_tail
          If True, compute the quantile for the left tail
          Otherwise, compute the quantile for the right tail
      Returns
      -------
      Tensor
          Quantiles tensor, of the same shape as alpha
      """
  
      F = self.F
  
      if left_tail:
          tail_a, tail_b = self.tail_al, self.tail_bl
      else:
          tail_a, tail_b = self.tail_ar, self.tail_br
          alpha = 1 - alpha
  
      if axis is not None:
          tail_a, tail_b = (
              F.expand_dims(tail_a, axis=axis),
              F.expand_dims(tail_b, axis=axis),
          )
  
      return F.broadcast_add(
          F.broadcast_mul(tail_a, F.log(alpha)), tail_b
      )
  
imports: from typing import Dict, List, Optional, Tuple
  import numpy
  from gluonts.core.component import validated
  from gluonts.mx import Tensor
  from gluonts.mx.util import cumsum
  from .bijection import AffineTransformation, Bijection
  from .distribution import Distribution, getF
  from .distribution_output import DistributionOutput
  from .transformed_distribution import TransformedDistribution
label_desc: Use image node_id 10 for calling the ISQF obj's underlying member method code with example usage: obj.quantile_tail(alpha, axis, left_tail) and returns: F