Method Of Medians For Life Time Data With Weibull Models

this paper protect us from erroneous values that may have crept into our data sets by human errors or sampling from some objects from a totally different population. The advantage of the method of medians estimator in the presence of outliers is also illustrated by applications to other real and simulated data. Because the medianbased estimator does not rely on the exact values in either side of the median, it can be especially useful when a small number of extreme values is censored or truncated. Although the method of MED is not developed here for random censoring in general, we show that about 16% of the largest or 34% of the smallest observations in a given sample may be right or left censored without affecting the value of the estimator. Unlike in the computation of the maximum likelihood estimator, no adjustment needs to be made in such problems for the method of medians estimator. Avoidance of more sophisticated statistical theory and methods for censored data can be a sure plus for some users. We use a simulation study to compare the method of medians estimator and the cross-checking method with the maximum likelihood estimator as well as the ANS estima3 tor recommended in Shier and Lawrence (1984). The study confirms that the maximum likelihood estimates are non-robust when upper or lower outliers are present in the data, especially when the underlying model has an increasing hazard function. The ANS estimator has a limited degree of robustness, but the method of medians shows the expected high degree of robustness at the cost of efficiency loss at the model. The cross-checking method provides a desirable level of compromise. It can be viewed as formalization of a very simple idea. That is, we are often better off by computing two different estimators for the s..