def f_cdf(x, df1, df2):
"""
Gives the value of the Fisher cumulative density function
for the given x (x must be in [0, inf))and the specified
parameters of the Fisher distribution- df1 and df2 specify
the degrees of freedom (d1 and d2 > 0).
"""
if df1 <= 0 or df2 <= 0:
raise IncorrectInputError()
index = df1*x/(df1*x+df2)
A = functions.incomplete_beta_function(index, df1/2, df2/2)
B = functions.beta_function(df1/2, df2/2)
return A/B
def f_pdf(x, df1, df2):
"""
Gives the value of the Fisher probability density function
for the given x (x must be in (0, inf))and the specified
parameters of the Fisher distribution- df1 and df2 specify
the degrees of freedom (d1 and d2 > 0).
TODO: implement for x = 0!
"""
if df1 <= 0 or df2 <= 0:
raise IncorrectInputError()
A = math.pow(df1*x, df1)
B = math.pow(df2, df2)
C = math.pow(df1*x+df2, df1+df2)
D = math.pow(A*B/C, 0.5)
beta = functions.beta_function(df1/2, df2/2)
return D/(x*beta)
