How to apply Henze-Zirkler's Multivariate Normality Test in Jupyter notebook with rpy2

This is another answer since I discover this method later. If you do not want to import the library of R into Python. One may call the output of R to python. i.e. one is capable of activating R function through python as follow:

import rpy2.robjects as robjects
from rpy2.robjects import r
from rpy2.robjects.numpy2ri import numpy2ri
from rpy2.robjects.packages import importr
import numpy as np

suppose that resi is a Dataframe in python say

# Create data
resi = pd.DataFrame(np.random.random((108, 2)), columns=['Number1','Number2'])

Then the code is as follow

#Converting the dataframe from python to R

# firt take the values of the dataframe to numpy
resi1=np.array(resi, dtype=float)

# Taking the variable from Python to R
r_resi = numpy2ri(resi1)

# Creating this variable in R (from python)
r.assign("resi", r_resi)

# Calling libraries in R 
r('library("MVN")')

# Calling a function in R (from python)
r("res <- hzTest(resi, qqplot = F)")

# Retrieving information from R to Python
r_result = r("res")

# Printing the output in python
print(r_result)

This will generate the output:

 Henze-Zirkler's Multivariate Normality Test 

--------------------------------------------- 

  data : resi 



  HZ      : 2.841424 

  p-value : 1.032563e-06 



  Result  : Data are not multivariate normal. 

---------------------------------------------

Update per 2021-08-25 There has been some API changes both to the MVN package and ro rpy2. The following works with MVN version 5.9 and rpy2 version 3.4.

"""Interface file to access the R MVN package"""

import numpy as np
import rpy2.robjects.packages as rpackages
from rpy2.robjects import numpy2ri
from rpy2.robjects.packages import importr
from rpy2.robjects.vectors import StrVector


# Install packages, if they are not already installed
packages_to_install_if_needed = ("MVN",)
utils = rpackages.importr("utils")
utils.chooseCRANmirror(ind=1)  # select the first mirror in the list
names_to_install = [x for x in packages_to_install_if_needed if not rpackages.isinstalled(x)]
if len(names_to_install) > 0:
    utils.install_packages(StrVector(names_to_install))

# load the package
mvn = importr("MVN")

# Generate data
np_arr = np.random.multivariate_normal(np.ones(2), np.eye(2), size=100)

# activate automatic conversion from numpy to rpy2 interface objects
numpy2ri.activate()

# perform the work
res = mvn.mvn(np_arr)
print(res)

outputting

$multivariateNormality
           Test        HZ   p value MVN
1 Henze-Zirkler 0.3885607 0.8343017 YES

$univariateNormality
              Test  Variable Statistic   p value Normality
1 Anderson-Darling  Column1     0.2443    0.7569    YES
2 Anderson-Darling  Column2     0.3935    0.3692    YES

$Descriptives
    n      Mean   Std.Dev    Median       Min      Max      25th     75th
1 100 0.9619135 1.0353688 1.0222279 -1.994833 3.679615 0.2696537 1.758255
2 100 0.7664778 0.9134449 0.8121996 -1.568635 2.648268 0.2068718 1.418113
        Skew    Kurtosis
1 -0.2123274 -0.16171832
2 -0.3718904 -0.05279222

There is an open source Python package called Pingouin that provides Henze-Zirkler multivariate normality test and is tested against R's MVM.

https://pingouin-stats.org/generated/pingouin.multivariate_normality.html

Example extracted from the docs:

import pingouin as pg
data = pg.read_dataset('multivariate')
X = data[['Fever', 'Pressure', 'Aches']]
pg.multivariate_normality(X, alpha=.05)
>>> HZResults(hz=0.5400861018514641, pval=0.7173686509624891, normal=True)