def stddev(mu,sigma,xi):
if(xi==0):
return extremevalue.random(mu,sigma)
if(sigma<=0):
raise ValueError("sigma must be positive")
if(xi>=1/2):
return float("infinity")
return sigma/xi*math.sqrt(math.gamma(1-2*xi)-math.gamma(1-xi)**2)
def mean(mu,sigma,xi):
if(xi==0):
return extremevalue.random(mu,sigma)
if(sigma<=0):
raise ValueError("sigma must be positive")
if(xi>=1):
return float("infinity")
return mu+sigma*(math.gamma(1-xi)-1)/xi
def kurtosis(mu,sigma,xi):
if(xi==0):
return extremevalue.random(mu,sigma)
if(sigma<=0):
raise ValueError("sigma must be positive")
if(xi>=1/4):
return float("infinity")
return (math.gamma(1-4*xi)-4*math.gamma(1-xi)*math.gamma(1-3*xi)+6*math.gamma(1-2*xi)*(math.gamma(1-xi)**2)-3*(math.gamma(1-xi)**4))/math.pow(math.gamma(1-2*xi)-math.gamma(1-xi)**2,2)-3
def skewness(mu,sigma,xi):
if(xi==0):
return extremevalue.random(mu,sigma)
if(sigma<=0):
raise ValueError("sigma must be positive")
if(xi>=1/3):
return float("infinity")
return (abs(xi)/xi)*(math.gamma(1-3*xi)-3*math.gamma(1-xi)*math.gamma(1-2*xi)+2*math.gamma(1-xi)**3)/math.pow(math.gamma(1-2*xi)-math.gamma(1-xi)**2,3/2)
def entropy(mu,sigma,xi):
if(xi==0):
return extremevalue.random(mu,sigma)
if(sigma<=0):
raise ValueError("sigma must be positive")
return math.log(sigma)+ds.euler_gamma*(xi+1)+1
def mode(mu,sigma,xi):
if(xi==0):
return extremevalue.random(mu,sigma)
if(sigma<=0):
raise ValueError("sigma must be positive")
return mu+sigma*(math.pow(1+xi,-xi)-1)/xi
def random(mu,sigma,xi):
if(xi==0):
return extremevalue.random(mu,sigma)
if(sigma<=0):
raise ValueError("sigma must be positive")
return mu+sigma*(math.pow(math.log(1/ds.rg0()),-xi)-1)/xi