code: def test_exponential_left_tail_approximation() -> None:
      tol = 1e-5
      x_coord = [0.1, 0.5, 0.9]
      y_coord = [
          np.array([0.1, 0.5, 1]),
          np.array([1.0, 2.0, 3.0]),
          np.array([0.25, 0.5, 0.9]),
      ]
      x = 0.01
      beta_inv = np.array([0.55920144, 0.9320024, 1.24266987])
      exact = beta_inv * np.log(x / x_coord[1]) + y_coord[1]
      exp_tail_approximation = ExponentialTailApproximation(
          x_coord, y_coord
      )
      assert np.all(
          np.abs(exact - exp_tail_approximation.left(x)) <= tol
      )
  
file_path: gluonts/test/model/test_forecast.py
imports: import numpy
  import pandas
  import pytest
  from gluonts.model.forecast import QuantileForecast, SampleForecast, _linear_interpolation, ExponentialTailApproximation
label_desc: Use image node_id 6 for calling a global function with example usage: test_exponential_left_tail_approximation() without return types