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