Maximum Likelihood Estimation for the Three Parameter Weibull Distribution Based on Censored Samples

This study develops maximum likelihood estimators for the three parameter Weibull distribution based on various left and right censored data situations. For the case of single censoring from the left and progressive censoring from the right the developed estimation procedure involves the simultaneous solution of two iterative equations compared to the arduous task of solving three simultaneous iterative equations as outlined by Harter and Moore [6]. For the two parameter Weibull [4], the above case results in an estimation procedure involving only one iterative equation. The asymptotic variance-covariance matrix of the estimators is given. Pivotal functions are provided whose distributions can be used for confidence interval estimation and for tests of hypotheses. An example is included which illustrates the estimation procedure involving left censored samples.