How to calculate the inverse of the normal cumulative distribution function in 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

User · Answer

given random variable X  house price  with population muy   60  sigma   40 import scipy as sc import scipy stats as sct sc version full version   0 15 1   a  Find P X lt 50  sct norm cdf x 50 loc 60 scale 40    0 4012936743170763   b  Find P X gt  50  sct norm sf x 50 loc 60 scale 40    0 5987063256829237   c  Find P 60 lt  X lt  80  sct norm cdf x 80 loc 60 scale 40  - sct norm cdf x 60 loc 60 scale 40    d  how much top most 5  expensive house cost at least  or find x where P X gt  x    0 05 sct norm isf q 0 05 loc 60 scale 40    e  how much top most 5  cheapest house cost at least  or find x where P X lt  x    0 05 sct norm ppf q 0 05 loc 60 scale 40

User · 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

User · Answer

Starting Python 3 8  the standard library provides the NormalDist object as part of the statistics module   It can be used to get the inverse cumulative distribution function  inv cdf - inverse of the cdf   also known as the quantile function or the percent-point function for a given mean  mu  and standard deviation  sigma    from statistics import NormalDist  NormalDist mu 10  sigma 2  inv cdf 0 95    13 289707253902943   Which can be simplified for the standard normal distribution  mu   0 and sigma   1    NormalDist   inv cdf 0 95    1 6448536269514715

[python] How to calculate the inverse of the normal cumulative distribution function in python?

Examples related to python

Examples related to scipy

Examples related to normal-distribution