def integrand(x):
log_p = base_dist.logpdf(x, df=k)
log_q = powerlaw.logpdf(x, a=k, loc=a, scale=L)
delta = log_p - log_q
v = mult0(np.exp(log_p), log_logistic(delta)) + \
mult0(np.exp(log_q), log_logistic(-delta))
return v
def mix_logpdf(x, k, a, L):
lp1 = base_dist.logpdf(x, df=k)
lp2 = powerlaw.logpdf(x, a=k, loc=a, scale=L)
logpdf = logsumexp([lp1, lp2]) + np.log(0.5)
return logpdf
def mix_logpdf(x, k, a, L):
lp1 = base_dist.logpdf(x, df=k)
lp2 = powerlaw.logpdf(x, a=k, loc=a, scale=L)
logpdf = logsumexp([lp1, lp2]) + np.log(0.5)
#logpdf_chk = np.log(0.5 * np.exp(lp1) + 0.5 * np.exp(lp2))
#print logpdf, logpdf_chk
#assert(np.allclose(logpdf, logpdf_chk))
return logpdf
def integrand_2(x):
log_p = base_dist.logpdf(x, df=k)
log_q = powerlaw.logpdf(x, a=k, loc=a, scale=L)
delta = log_p - log_q
v = np.exp(log_q) * log_logistic(-delta)
return v
def integrand(x):
pp = powerlaw.pdf(x, a=k, loc=a, scale=L)
v = pp * (powerlaw.logpdf(x, a=k, loc=a, scale=L) -
mix_logpdf(x, k, a, L))
return v