def cvar_beta_variable(rv, beta):
"""
cvar of Beta variable on [0,1]
"""
qq = rv.ppf(beta)
scales, shapes = get_distribution_info(rv)[1:]
qq = (qq - scales["loc"]) / scales["scale"]
g1, g2 = shapes["a"], shapes["b"]
cvar01 = ((1 - betainc(1 + g1, g2, qq)) * gamma_fn(1 + g1) * gamma_fn(g2) /
gamma_fn(1 + g1 + g2)) / (beta_fn(g1, g2) * (1 - beta))
return cvar01 * scales["scale"] + scales["loc"]
def beta_pdf_derivative(alpha_stat, beta_stat, x):
"""
x in [0,1]
"""
#beta_const = gamma_fn(alpha_stat+beta_stat)/(
# gamma_fn(alpha_stat)*gamma_fn(beta_stat))
beta_const = 1. / beta_fn(alpha_stat, beta_stat)
deriv = 0
if alpha_stat > 1:
deriv += (alpha_stat - 1) * (x**(alpha_stat - 2) *
(1 - x)**(beta_stat - 1))
if beta_stat > 1:
deriv -= (beta_stat - 1) * (x**(alpha_stat - 1) *
(1 - x)**(beta_stat - 2))
deriv *= beta_const
return deriv
def beta_pdf(alpha_stat, beta_stat, x):
#scipy implementation is slow
const = 1. / beta_fn(alpha_stat, beta_stat)
return const * (x**(alpha_stat - 1) * (1 - x)**(beta_stat - 1))