def __init__(self, beta : float = None, eta : float = None):

self._beta = eta;

self._eta = eta;

@property

def beta(self) -> float:

return self._beta;

@property

def eta(self) -> float:

return self._eta;

def _getLikelihood(self, x : np.ndarray, theta : np.ndarray) -> float:

n = len(x);

beta, eta = theta[0], theta[1];

return n * (math.log(beta) - beta * math.log(eta)) + (beta - 1) * np.sum(np.log(x)) - np.sum(np.power(x / eta, beta));

def _getGradient(self, x : np.ndarray, theta : np.ndarray) -> np.ndarray:

n = len(x);

beta, eta = theta[0], theta[1];

dBeta = n * (1 / beta - math.log(eta)) + np.sum(np.log(x)) - np.sum(np.power(x / eta, beta) * np.log(x / eta));

dEta = (np.sum(np.power(x / eta, beta)) - n) * beta / eta;

return np.array([dBeta, dEta]).reshape(2, 1);

def _getHessian(self, x : np.ndarray, theta : np.ndarray) -> np.ndarray:

n = len(x);

beta, eta = theta[0], theta[1];

dBeta2 = -1 * (n / (beta ** 2) + np.sum(np.power(x / eta, beta) * np.square(np.log(x / eta))));

dEta2 = (n - (1 + beta) * np.sum(np.power(x / eta, beta))) * beta / (eta ** 2);

dBetaEta = (np.sum(np.power(x / eta, beta) * (1 + beta * np.log(x / eta))) - n) / eta;

return np.array([dBeta2, dBetaEta, dBetaEta, dEta2]).reshape(2, 2);

def _fitOLS(self, x : np.ndarray):

x = np.sort(x, axis = None);

n = len(x);

lr = LinearRegression();

lr.fit(np.mat(np.log(x).reshape(-1, 1)), np.mat(np.array([math.log(-math.log(1 - (k + 1) / (n + 1))) for k in range(n)]).reshape(-1, 1)));

self._beta = lr.beta[1, 0];

self._eta = math.exp(-lr.beta[0, 0] / lr.beta[1, 0]);

def _fitMLE(self, x : np.ndarray, epsilon : float = 10e-6, verbose : bool = False):

theta = 0.001 * np.random.rand(2);

count = 0;

g = self._getGradient(x, theta);

while np.linalg.norm(g, ord = None) > epsilon:

H = self._getHessian(x, theta);

theta -= (np.linalg.inv(H) @ g).flatten();

if np.any(theta < 0):

theta = 0.001 * np.random.rand(2);

g = self._getGradient(x, theta);

l = self._getLikelihood(x, theta);

count += 1;

if verbose:

print(f"iteration {count}, log-likelihood: {l}, gradient: {g.flatten()}");

self._beta, self._eta = theta[0], theta[1];

def fit(self, x : np.ndarray, method : WeibullDistributionFitMethod = WeibullDistributionFitMethod.MLE, epsilon : float = 10e-6, verbose : bool = False):

if x is None or len(x) == 0:

raise ValueError("x is none or empty");

if method == WeibullDistributionFitMethod.OLS:

self._fitOLS(x);

elif method == WeibullDistributionFitMethod.MLE:

self._fitMLE(x, epsilon, verbose);

else: