inverse_normal_distribution()

audmath.inverse_normal_distribution(y)

Inverse normal distribution.

Returns the argument $x$ for which the area under the Gaussian probability density function is equal to $y$. It returns $\text{nan}$ if $y \notin [0, 1]$.

The area under the Gaussian probability density function is given by:

$$\frac{1}{\sqrt{2\pi}} \int_{-\infty}^x \exp(-t^2 / 2)\,\text{d}t$$

This function is a numpy port of the Cephes C code. Douglas Thor implemented it in pure Python under GPL-3.

The output is identical to the implementation provided by scipy.special.ndtri(), and scipy.stats.norm.ppf(), and allows you to avoid installing and importing scipy. audmath.inverse_normal_distribution() is slower for large arrays as the following comparison of execution times on a standard PC show.

Samples	scipy	audmath
10.000	0.00s	0.01s
100.000	0.00s	0.09s
1.000.000	0.02s	0.88s
10.000.000	0.25s	9.30s

Parameters

y (Union[int, float, Sequence, ndarray]) – input value

Return type

Union[floating, ndarray]

Returns

inverted input

Examples

>>> inverse_normal_distribution([0.05, 0.4, 0.6, 0.95])
array([-1.64485363, -0.2533471 , 0.2533471 , 1.64485363])