# [SciPy-User] multivariate empirical distribution function, avoid double loop ?

Alan G Isaac alan.isaac@gmail....
Wed Aug 24 13:27:15 CDT 2011

```On 8/24/2011 10:23 AM, josef.pktd@gmail.com wrote:
> Does anyone know whether there is an algorithm that avoids the double
> loop to get a multivariate empirical distribution function?

I think that is pretty standard.
I'll attach something posted awhile ago.
It seemed right at the time, but I did
not test it.  Once upon a time it was at
http://svn.scipy.org/svn/scipy/trunk/scipy/sandbox/dhuard/stats.py

Cheers,
Alan

def empiricalcdf(data, method='Hazen'):
"""Return the empirical cdf.

Methods available (here i goes from 1 to N)
Hazen:       (i-0.5)/N
Weibull:     i/(N+1)
Chegodayev:  (i-.3)/(N+.4)
Cunnane:     (i-.4)/(N+.2)
Gringorten:  (i-.44)/(N+.12)
California:  (i-1)/N

:author: David Huard
"""
i = np.argsort(np.argsort(data)) + 1.
nobs = len(data)
method = method.lower()
if method == 'hazen':
cdf = (i-0.5)/nobs
elif method == 'weibull':
cdf = i/(nobs+1.)
elif method == 'california':
cdf = (i-1.)/nobs
elif method == 'chegodayev':
cdf = (i-.3)/(nobs+.4)
elif method == 'cunnane':
cdf = (i-.4)/(nobs+.2)
elif method == 'gringorten':
cdf = (i-.44)/(nobs+.12)
else:
raise 'Unknown method. Choose among Weibull, Hazen, Chegodayev, Cunnane, Gringorten and California.'
return cdf

```