def Beta(a, b, lo=0, up=1):
R"""
Beta Probability Distribution
Parameters
----------
a : float, Dist
First shape parameter
a > 0
b : float, Dist
Second shape parameter
b > 0
lo : float, Dist
Lower threshold
up : float, Dist
Upper threshold
Examples
--------
>>> cp.seed(1000)
>>> f = cp.Beta(2, 2, 2, 3)
>>> q = np.linspace(0,1,6)[1:-1]
>>> print f.inv(q)
[ 2.28714073 2.43293108 2.56706892 2.71285927]
>>> print f.fwd(f.inv(q))
[ 0.2 0.4 0.6 0.8]
>>> print f.sample(4)
[ 2.60388804 2.21123197 2.86505298 2.48812537]
>>> print f.mom(1)
2.5
"""
dist = co.beta(a, b) * (up - lo) + lo
dist.addattr(str="Beta(%s,%s,%s,%s)" % (a, b, lo, up))
return dist
def Beta(a, b, lo=0, up=1):
R"""
Beta Probability Distribution
Parameters
----------
a : float, Dist
First shape parameter
a > 0
b : float, Dist
Second shape parameter
b > 0
lo : float, Dist
Lower threshold
up : float, Dist
Upper threshold
Examples
--------
>>> cp.seed(1000)
>>> f = cp.Beta(2, 2, 2, 3)
>>> q = np.linspace(0,1,6)[1:-1]
>>> print f.inv(q)
[ 2.28714073 2.43293108 2.56706892 2.71285927]
>>> print f.fwd(f.inv(q))
[ 0.2 0.4 0.6 0.8]
>>> print f.sample(4)
[ 2.60388804 2.21123197 2.86505298 2.48812537]
>>> print f.mom(1)
2.5
"""
dist = co.beta(a, b)*(up-lo) + lo
dist.addattr(str="Beta(%s,%s,%s,%s)" % (a,b,lo,up))
return dist
def Wigner(radius=1, shift=0):
"""
Wigner (semi-circle) distribution
radius : float, Dist
radius of the semi-circle (scale)
shift : float, Dist
location of the origen (location)
"""
dist = radius*(2*co.beta(1.5,1.5)-1) + shift
dist.addattr(str="Wigner(%s,%s)" % (radius, shift))
return dist
def Wigner(radius=1, shift=0):
"""
Wigner (semi-circle) distribution
radius : float, Dist
radius of the semi-circle (scale)
shift : float, Dist
location of the origen (location)
"""
dist = radius * (2 * co.beta(1.5, 1.5) - 1) + shift
dist.addattr(str="Wigner(%s,%s)" % (radius, shift))
return dist
def Arcsinus(shape=0.5, lo=0, up=1):
"""
Generalized Arc-sinus distribution
shape : float, Dist
Shape parameter where 0.5 is the default non-generalized case.
lo : float, Dist
Lower threshold
up : float, Dist
Upper threshold
"""
dist = co.beta(shape, 1-shape)*(up-lo) + lo
dist.addattr(str="Arcsinus(%s,%s,%s)" % (shape, lo, up))
return dist
def Arcsinus(shape=0.5, lo=0, up=1):
"""
Generalized Arc-sinus distribution
shape : float, Dist
Shape parameter where 0.5 is the default non-generalized case.
lo : float, Dist
Lower threshold
up : float, Dist
Upper threshold
"""
dist = co.beta(shape, 1 - shape) * (up - lo) + lo
dist.addattr(str="Arcsinus(%s,%s,%s)" % (shape, lo, up))
return dist
def Powerlaw(shape=1, lo=0, up=1):
"""
Powerlaw distribution
Parameters
----------
shape : float, Dist
Shape parameter
lo : float, Dist
Location of lower threshold
up : float, Dist
Location of upper threshold
"""
dist = co.beta(shape, 1)*(up-lo) + lo
dist.addattr(str="Powerlaw(%s,%s,%s)"%(shape, lo, up))
return dist
def Powerlaw(shape=1, lo=0, up=1):
"""
Powerlaw distribution
Parameters
----------
shape : float, Dist
Shape parameter
lo : float, Dist
Location of lower threshold
up : float, Dist
Location of upper threshold
"""
dist = co.beta(shape, 1) * (up - lo) + lo
dist.addattr(str="Powerlaw(%s,%s,%s)" % (shape, lo, up))
return dist
