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# scipy.special.ndtri_exp

scipy.special.ndtri_exp(y, out=None) = <ufunc 'ndtri_exp'>

  Inverse of `log_ndtr` vs x. Allows for greater precision than `ndtri` composed with `numpy.exp` for very small values of y and for y close to 0.

  Parameters:
    yarray_like of float

      Function argument

    outndarray, optional

      Optional output array for the function results

  Returns:
    scalar or ndarray

      Inverse of the log CDF of the standard normal distribution, evaluated at y.

  See also

  `log_ndtr`

    log of the standard normal cumulative distribution function

  `ndtr`

    standard normal cumulative distribution function

  `ndtri`

    standard normal percentile function

  Examples

      >>> import numpy as np
      >>> import scipy.special as sc

  `ndtri_exp` agrees with the naive implementation when the latter does not suffer from underflow.

      >>> sc.ndtri_exp(-1)
      -0.33747496376420244
      >>> sc.ndtri(np.exp(-1))
      -0.33747496376420244

  For extreme values of y, the naive approach fails

      >>> sc.ndtri(np.exp(-800))
      -inf
      >>> sc.ndtri(np.exp(-1e-20))
      inf

  whereas `ndtri_exp` is still able to compute the result to high precision.

      >>> sc.ndtri_exp(-800)
      -39.88469483825668
      >>> sc.ndtri_exp(-1e-20)
      9.262340089798409