Fast generation of COrrelated Non-NOrmal RAndom Variates (CONNORAV)

Specify your distributions in terms of mean, standard deviation, skew, kurtosis and a correlation matrix. CONNORAV can generate random variates fitting these distribution descriptions in a fast and accurate manner.

Requirements

• Python >= 3.8
• NumPy:
  • For Python < 3.10: >=1.22,<2.0
  • For Python >= 3.10: >=1.26 (2.x supported)
• SciPy:
  • For Python < 3.10: >=1.10,<1.12
  • For Python >= 3.10: >=1.13

Motivation

Fitting a distribution to mean, standard deviation, skew and kurtosis is a surprisingly tricky proposition, which is a little surprising since these are the most common descriptors used when describing non-normal distributions. CONNORAV achieves this using the optimization techinique described by Tuenter (2001) to fit these statistics to an analytical Johnson SU distribution.

• We match the first four moments to a Johnson SU distribution using:
• H. J. H. Tuenter (2001), “An algorithm to determine the parameters of SU-curves in the Johnson system of probability distributions by moment matching.”

While it is true that not all distributions can be described using mean, standard deviation, skew and kurtosis alone, a lot of data resembles these shapes and the statistics are very easy to measure.

Once the distributions have been specified, non-normal correlated random variates can be generated via the copula trick. This is extremely useful for monte-carlo analysis and risk assessment.

Examples

Generate a distribution and test the random number generator.

In [1]: from connorav import MSSKDistribution

In [2]: dist = MSSKDistribution(2.5,1.3,-0.3,2.0)

Alternatively you can construct using an array or tuple

In [2]: dist = MSSKDistribution([2.5,1.3,-0.3,2.0])

In [3]: dist.mean()
Out[3]: 2.4999999999942295

In [4]: dist.std()
Out[4]: 1.3000000000127732

In [5]: samples = dist.rvs(100000)

In [6]: samples.mean()
Out[6]: 2.4958419823009592

In [7]: samples.std()
Out[7]: 1.2991039572289937

In [8]: from scipy.stats import skew, kurtosis

In [9]: skew(samples)
Out[9]: -0.2879332050448415

In [10]: kurtosis(samples)
Out[10]: 1.926596584590544

Lets generate some numbers.

In [1]: import numpy

In [2]: from connorav import CorrelatedNonNormalRandomVariates

In [3]: num_samples = 200000

In [4]: # The desired covariance matrix.

In [5]: correlations = numpy.array([
   ...:         [  1.00,  0.60,  0.30],
   ...:         [  0.60,  1.00,  0.50],
   ...:         [  0.30,  0.50,  1.00]
   ...:     ])


In [7]: moments = numpy.array([[0.0,1.0,0.0,0.0],[14.0,0.9,0.8,1.8],[7.9,0.3,0.2,1.6]])


In [8]: rv_generator = CorrelatedNonNormalRandomVariates(moments,correlations,num_samples)
Normal

In [9]: rv = rv_generator.rv

In [11]: x = numpy.corrcoef(rv)

In [12]: print x
[[ 1.          0.58994313  0.29320107]
 [ 0.58994313  1.          0.48837508]
 [ 0.29320107  0.48837508  1.        ]]


In [13]: from scipy.stats import skew, kurtosis

In [14]: for i in range(3):
   ....:         print "Moments",i
   ....:         print rv[i,:].mean()
   ....:         print rv[i,:].std()
   ....:         print skew(rv[i,:])
   ....:         print kurtosis(rv[i,:])
   ....:
Moments 0
0.00153746238126
0.999078801649
-0.0016863652429
-0.0135121492172
Moments 1
13.9980416496
0.894414387863
0.805404037664
1.8027042337
Moments 2
7.90077062606
0.29955446882
0.215294195427
1.61036003402

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Created by Christopher Bates