COMPARISON OF VARIOUS ESTIMATORS FOR WEIBULL PARAMETERS BY SUPPLYING PREDICTED VALUES OF UNKNOWN DATA FROM DOUBLY CENSORED SMALL SAMPLES : Use of Empirical Method of Improvement for |BIAS| and MSE

Abstract

Recently in the literature [8] we have proposed fairly good methods of estimating especially the scale parameter of the Weibull distribution from right censored type II data, whereas in the present paper we shall study the same kind of problems and compare 12×5+8=68 kinds of the results of |BIAS| and MSE yielded by the combination of the eight methods of estimation and the five plus three data-types of unknown data predictions through performing N=20000 trials of simulation for each of the sample sizes n=5,7,10,15,20 and for more than 4 observed data. In most cases of the primal stage of our simulation with sample sizes n=5,7,10,15 and censored observations considered here, the estimator MPM defined in Sec.2.5 may be recommended, while in many cases of the stage of the size n=20, LSE in Sec.2.2 may be proposed, as the most desirable estimator among many candidates in each of the respective cases. However, if MSE/m^2 of the estimator obtained in the stage is not small, the reader may proceed to the second stage to use our EMI (Empirical Method of Improvement) shown in Sec.2.8 and Appendix.