r""" Calculates the mean of the Gumbel LEV distribution with given parameters. .. math:: E = \mu + \sigma\gamma

Maximum Likelihood Estimation (MLE)

MOM: Method of Moments. This is one of the simplest ways to calculate the parameters of a distribution. This method is quick but only wo

r""" n-th moment of the Weibull distribution .. math:: M(n) = \alpha^n \Gamma \left ( 1 + \frac{n}{\beta} \right )

r""" n-th moment of the Bernoulli distribution .. math:: M(n) = p Parameters ---------- n : in

r""" n-th (non central) moment of the LogNormal distribution .. math:: E = ... complicated. Parameters

r""" n-th (non central) moment of the Uniform distribution .. math:: M(n) = \frac{1}{n +1} \sum_{i=0}^{n}a^ib^{n-i}

r""" n-th (non central) moment of the Beta distribution .. math:: E = \frac{B \left( n + \alpha, \beta \right )}{B

r""" Calculates the n-th moment of the Gamma distribution with given parameters. .. math:: E = \frac{\Gamma \lef

r""" n-th (non central) moment of the Normal distribution .. math:: E = ... complicated. Parameters ---

r""" m-th (raw) moment of the Binomial distribution. Parameters ---------- m : integer The ordinal of t

r""" Calculates the n-th moment of the Exponential distribution. .. math:: E = \frac{n!}{\lambda^{n}} Parameter

r""" m-th (non central) moment of the four-parameter Beta distribution. Computed from the standard Beta moments via the binomial

r""" n-th moment of the Rayleigh distribution .. math:: M(n) = \sigma^n 2^{n/2} \Gamma \left ( 1 + \frac{n}{2} \right )

MPP: Method of Probability Plotting This is the classic probability plotting paper method. This method creates the plotting points, tran

MPS: Maximum Product Spacing This is the method to get the largest (geometric) average distance between all points. This method works re

MSE: Mean Square Error This is simply fitting the curve to the best estimate from a non-parametric estimate. This is slightly differ

Aalen's (Poisson) estimate of the variance of the Nelson-Aalen cumulative hazard estimator: Var(H) = sum(d / r**2) Recommended by K

Starting parameter vector for the optimiser given event times.

This is the Breslow implementation TODO: - Efron, and - Kalbfleisch and Prentice (This is what we need!)