def pdf(x, mu=0, sigma=1):
"""
Log-normal distribution probability density function.
"""
_validate_sigma(sigma)
if x <= 0:
return mpmath.mp.zero
x = mpmath.mpf(x)
lnx = mpmath.log(x)
return mpmath.npdf(lnx, mu, sigma) / x
def pdf(x, a, b):
"""
PDF of the truncated standard normal distribution.
"""
_validate_params(a, b)
if x < a or x > b:
return mpmath.mp.zero
with mpmath.extradps(5):
x = mpmath.mpf(x)
a = mpmath.mpf(a)
b = mpmath.mpf(b)
delta = _norm_delta_cdf(a, b)
return mpmath.npdf(x) / delta
def var(chi, c):
"""
Variance of the ARGUS distribution.
"""
if c <= 0:
raise ValueError('c must be positive')
if chi <= 0:
raise ValueError('chi must be positive')
with mpmath.extradps(5):
chi = mpmath.mpf(chi)
c = mpmath.mpf(c)
mu = mean(chi, c)
t1 = c**2 * (mpmath.mp.one - 3 / chi**2 +
chi * mpmath.npdf(chi) / _psi(chi))
return t1 - mu**2
def pHit(z,
zReal,
desvioHit=(Parametros.DESVIO_HIT),
alcanceMax=(Parametros.ALCANCE_MAXIMO)):
if (0 <= z <= alcanceMax):
#n = (mp.ncdf(alcanceMax,zReal,desvioHit) - mp.ncdf(0,zReal,desvioHit))**-1 #ta errado
'''
Usar uma area e calcular ncdf ao invez de npdf
a probabilidade de um ponto eh zero, mas a valor da funcao nao eh
'''
#print "N ", n
aux = 0
#for i in range(alcanceMax*10):
# aux += mp.npdf(float(i)/10,zReal,desvioHit)
#print "AREA ", aux
#n = aux**-1
n = 0.1
#print "Com: ", (mp.ncdf(z+0.01,zReal,desvioHit - mp.ncdf(z-0.01,zReal,desvioHit))), "Sem: ", n*mp.npdf(z,zReal,desvioHit)
return n * mp.npdf(z, zReal, desvioHit)
#return (mp.ncdf(z+0.01,zReal,desvioHit - mp.ncdf(z-0.01,zReal,desvioHit)))
else:
return 0
def _mu1(x):
return mp.npdf(x, mu=1, sigma=sigma)
def _mu0(x):
return mp.npdf(x, mu=0, sigma=sigma)
def f49(x):
# hazard
return mpmath.npdf(x) / (1 - mpmath.ncdf(x))
def f47(x):
# erf_Z
return mpmath.npdf(x)
def mu0(x): return mpmath.npdf(x, mu=0, sigma=sigma)
def pdf(x, mu=0, sigma=1):
"""
Normal distribution probability density function.
"""
# Defined here for consistency, but this is just mpmath.npdf
return mpmath.npdf(x, mu, sigma)
def _psi(chi):
return mpmath.ncdf(chi) - chi * mpmath.npdf(chi) - mpmath.mpf('0.5')
