[Numpy-discussion] pareto docstring

[josef.pktd at gmail.com]

Assuming no typos

Relationship between Pareto, Pareto(II)/Lomax and Generalized Pareto,GPD

>>> import sympy as sy
>>> x = sy.Symbol('x')
>>> k = sy.Symbol('k')
>>> c = sy.Symbol('c')
>>> a = sy.Symbol('a')
>>> m = sy.Symbol('m')
>>> mgpd = sy.Symbol('mgpd')

>>> gpd0 = (1 - c*x/k)**(1/c - 1)/k  #JKB notation (c reversed sign)
>>> gpd = 1/k/(1 + c*(x-mgpd)/k)**(1/c + 1) #similar to Wikipedia
>>> par = a*k**a/(x-m)**(1+a)  #JKB
>>> lom = a/k/(1+x/k)**(1+a)

>>> lom.subs(k,1)  #Pareto(II), Lomax  (loc=0, scale=1)
a*(1 + x)**(-1 - a)
>>> par.subs(k,1).subs(m,-1)  #Pareto with loc=-1, scale=1
a*(1 + x)**(-1 - a)
>>> gpd.subs(c,1/a).subs(k,1/a).subs(mgpd,0) #GPD with loc=0, scale=1/a
a*(1 + x)**(-1 - a)


>>> par.subs(k,1).subs(m,0)  # standard Pareto (loc=0, scale=1)
a*x**(-1 - a)
>>> gpd.subs(c,1/a).subs(k,1/a).subs(mgpd,1) #GPD with loc=1, scale=1/a
a*x**(-1 - a)

Josef