def chi_high(x, df):
"""Returns right-hand tail of chi-square distribution (x to infinity).
df, the degrees of freedom, ranges from 1 to infinity (assume integers).
Typically, df is (r-1)*(c-1) for a r by c table.
Result ranges from 0 to 1.
See Cephes docs for details.
"""
x = fix_rounding_error(x)
if x < 0:
raise ValueError("chi_high: x must be >= 0 (got %s)." % x)
if df < 1:
raise ValueError("chi_high: df must be >= 1 (got %s)." % df)
return igamc(df / 2, x / 2)
def chi_high(x, df):
"""Returns right-hand tail of chi-square distribution (x to infinity).
df, the degrees of freedom, ranges from 1 to infinity (assume integers).
Typically, df is (r-1)*(c-1) for a r by c table.
Result ranges from 0 to 1.
See Cephes docs for details.
"""
x = fix_rounding_error(x)
if x < 0:
raise ValueError("chi_high: x must be >= 0 (got %s)." % x)
if df < 1:
raise ValueError("chi_high: df must be >= 1 (got %s)." % df)
return igamc(df / 2, x / 2)
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
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