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STAB
====

Simulation and estimation of stable scalar variables.


TUTORIAL
--------

# install
!pip install pystab

# import
import stab

# generate one million normal samples
x = stab.stables(2, 0, 10**6)

# estimate the four parameters from the vector x
stab.fit_quantiles(x)
> (1.9972697816715559,
   0.018033003626273775,
   0.9993768437879497,
   -0.000605309795968803)

# generate one million Lévy samples
x = stab.stables(0.5, 1, 10**6)

# estimate the parameters
# (notice that the shift parameter is imprecise due to heavy tails)
stab.fit_quantiles(x)
> (0.5000056240198412,
   0.9998393548232919,
   0.9901156603367183,
   1.0144504595708657)


DOCUMENTATION
-------------

# core functions

stable(α, β):     # Return a S(α,β,1,0) pseudorandom sample, α∈[2,0[, β∈[-1,1]
stables(α, β):    # Return a vector with n stable samples i.i.d. S(α,β,1,0)
fit_quantiles(x): # Return a tuple (α,β,σ,μ) with the estimated 4 parameters


# convenience functions

uniform():        # Return a U(0,1) pseudorandom sample
normal():         # Return a N(0,1) pseudorandom sample
stable4(α,β,c,μ): # Return a S(α,β,c,μ) pseudorandom sample

uniforms(n):         # Return vector with n pseudorandom samples i.i.d. U(0,1)
normals(n):          # Return vector with n pseudorandom samples i.i.d. N(0,1)
stables4(α,β,c,μ,n): # Return vector with n stable samples i.i.d. S(α,β,c,μ)



ACKNOWLEDGEMENT
---------------

Reference: https://en.wikipedia.org/wiki/Stable_distribution

The simulation algorithm is that of Chambers-Mallows-Struck and Weron

The estimation algorithm is McCulloch's quantile method, using the GPL
implementation in C by Royuela.

- McCulloch's original implemantation in GAUSS: https://www.asc.ohio-state.edu/mcculloch.2/programs/STAB

- Royuela's website: http://www.lpi.tel.uva.es/~jroyval/



RELEASING
---------

To update the pypi hub, you need an account on pypi, and then run the following
commands:

	cd pypi
        # update version number on file setup.py
        # update version number on file stab.py
	python setup.py sdist bdist_wheel
	python -m twine upload dist/pystab-X.tar.gz
	rm -rf build dist pystab.egg-info