Example #1
0
def bdtri(k, n, y):
    """Inverse of binomial distribution.

    Finds binomial p such that sum of terms 0-k reaches cum probability y.
    """
    y = fix_rounding_error(y)
    if y < 0.0 or y > 1.0:
        raise ZeroDivisionError, "y must be between 1 and 0."
    if k < 0 or n <= k:
        raise ZeroDivisionError, "k must be between 0 and n"
    dn = n - k
    if k == 0:
        if y > 0.8:
            p = -expm1(log1p(y-1.0) / dn)
        else:
            p = 1.0 - y**(1.0/dn)
    else:
        dk = k + 1;
        p = incbet(dn, dk, 0.5)
        if p > 0.5:
            p = incbi(dk, dn, 1.0-y)
        else:
            p = 1.0 - incbi(dn, dk, y)
    return p
Example #2
0
def bdtrc(k, n, p):
    """Complement of binomial distribution, k+1 through n.

    Uses formula bdtrc(k, n, p) = betai(k+1, n-k, p)

    See Cephes docs for details.
    """
    p = fix_rounding_error(p)
    if (p < 0) or (p > 1):
        raise ValueError, "Binomial p must be between 0 and 1."
    if (k < 0) or (n < k):
        raise ValueError, "Binomial k must be between 0 and n."
    if k == n:
        return 0
    dn = n - k
    if k == 0:
        if p < .01:
            dk = -expm1(dn * log1p(-p))
        else:
            dk = 1 - pow(1.0-p, dn)
    else:
        dk = k + 1
        dk = betai(dk, dn, p)
    return dk