Weibull and Reliability/Failure Time Analysis - Notes and Technical Information
Standard references and textbooks describing these techniques include Lawless (1982), Nelson (1990), Lee (1980), and Dodson (1994).
The specific methods for estimating the parameters for the Weibull distribution are described in Dodson (1994).
A detailed description of a Newton-Raphson iterative method, similar to the one used in Statistica , for estimating the maximum likelihood parameters for the two-parameter distribution is provided in Keats and Lawrence (1997).
The estimation of the location parameter for the three-parameter Weibull distribution poses a number of special problems, which are detailed in Lawless (1982).
The (optional) weighted least squares methods algorithm for fitting the Weibull distribution to grouped data is described in Gehan and Siddiqui (1973) and Lee (1992).
For details concerning the Weibull distribution, see the description of the Weibull CDF, reliability, and hazard functions. The computational formulas for computing the nonparametric estimates of the cumulative distribution function for censored failure time data are described in Failure Order for Single or Uncensored Data and Modified Failure Order for Multiple-Censored Data.