l_pdf, r_pdf = left**x*(1-left)**(n-x), right**x*(1-right)**(n-x)
return (r_pdf - l_pdf)*r_pdf/(dkpdf(right)*l_pdf - dkpdf(left)*r_pdf)
left_max = special.betaincinv(x+1, n-x+1, 1 - conf)
- left = find_root(f, left_max/2, 8, (0, left_max))
+ left = find_root(f, special.betaincinv(x+1, n-x+1, (1 - conf)/2), 8, (0, special.betaincinv(x+1, n-x+1, 1 - conf)))
return left, special.betaincinv(x+1, n-x+1, special.betainc(x+1, n-x+1, left) + conf)
def binomial_conf_center_radius(x, n, conf=0.95):