Yueyoum - 6 months ago 506

Python Question

How do I calculate the inverse of the cumulative distribution function (CDF) of the normal distribution in Python?

Which library should I use? Possibly scipy?

Answer

NORMSINV (mentioned in a comment) is the inverse of the CDF of the standard normal distribution. Using `scipy`

, you can compute this with the `ppf`

method of the `scipy.stats.norm`

object. The acronym `ppf`

stands for *percent point function*, which is another name for the *quantile function*.

```
In [20]: from scipy.stats import norm
In [21]: norm.ppf(0.95)
Out[21]: 1.6448536269514722
```

Check that it is the inverse of the CDF:

```
In [34]: norm.cdf(norm.ppf(0.95))
Out[34]: 0.94999999999999996
```

By default, `norm.ppf`

uses mean=0 and stddev=1, which is the "standard" normal distribution. You can use a different mean and standard deviation by specifying the `loc`

and `scale`

arguments, respectively.

```
In [35]: norm.ppf(0.95, loc=10, scale=2)
Out[35]: 13.289707253902945
```

If you look at the source code for `scipy.stats.norm`

, you'll find that the `ppf`

method ultimately calls `scipy.special.ndtri`

. So to compute the inverse of the CDF of the standard normal distribution, you could use that function directly:

```
In [43]: from scipy.special import ndtri
In [44]: ndtri(0.95)
Out[44]: 1.6448536269514722
```