def Lognormal(mu=0, sigma=1, shift=0, scale=1):
R"""
Log-normal distribution
Parameters
----------
mu : float, Dist
Mean in the normal distribution.
Overlaps with scale by mu=log(scale)
sigma : float, Dist
Standard deviation of the normal distribution.
shift : float, Dist
Location of the lower bound.
scale : float, Dist
Scale parameter.
Overlaps with mu by scale=e**mu
Examples
--------
>>> cp.seed(1000)
>>> f = cp.Lognormal(0, 1)
>>> q = np.linspace(0,1,6)[1:-1]
>>> print f.inv(q)
[ 0.43101119 0.77619841 1.28833038 2.32012539]
>>> print f.fwd(f.inv(q))
[ 0.2 0.4 0.6 0.8]
>>> print f.sample(4)
[ 1.48442856 0.30109692 5.19451094 0.95632796]
>>> print f.mom(1)
1.6487212707
"""
dist = co.lognormal(sigma)*scale*np.e**mu + shift
dist.addattr(str="Lognormal(%s,%s,%s,%s)"%(mu,sigma,shift,scale))
return dist
def Lognormal(mu=0, sigma=1, shift=0, scale=1):
R"""
Log-normal distribution
Parameters
----------
mu : float, Dist
Mean in the normal distribution.
Overlaps with scale by mu=log(scale)
sigma : float, Dist
Standard deviation of the normal distribution.
shift : float, Dist
Location of the lower bound.
scale : float, Dist
Scale parameter.
Overlaps with mu by scale=e**mu
Examples
--------
>>> cp.seed(1000)
>>> f = cp.Lognormal(0, 1)
>>> q = np.linspace(0,1,6)[1:-1]
>>> print f.inv(q)
[ 0.43101119 0.77619841 1.28833038 2.32012539]
>>> print f.fwd(f.inv(q))
[ 0.2 0.4 0.6 0.8]
>>> print f.sample(4)
[ 1.48442856 0.30109692 5.19451094 0.95632796]
>>> print f.mom(1)
1.6487212707
"""
dist = co.lognormal(sigma) * scale * np.e**mu + shift
dist.addattr(str="Lognormal(%s,%s,%s,%s)" % (mu, sigma, shift, scale))
return dist
def Gilbrat(scale=1, shift=0):
"""
Gilbrat distribution
Standard log-normal distribution
Parameters
----------
scale : float, Dist
Scaling parameter
shift : float, Dist
Location parameter
"""
dist = co.lognormal(1)*scale + shift
dist.addattr(str="Gilbrat(%s,%s)"%(scale, shift))
return dist
def Gilbrat(scale=1, shift=0):
"""
Gilbrat distribution
Standard log-normal distribution
Parameters
----------
scale : float, Dist
Scaling parameter
shift : float, Dist
Location parameter
"""
dist = co.lognormal(1) * scale + shift
dist.addattr(str="Gilbrat(%s,%s)" % (scale, shift))
return dist
