Abstract
Several methods have been used to estimate the unknown parameters in the two-parameter exponential distribution. Here we have considered two of these methods, maximum likelihood method and median-first order statistics method. However, in the presence of outliers these methods are not valid. In this paper we propose two approaches that deal with this situation. The idea is based on using first and third quartile instead of the minimum statistics. We investigated the parameters estimate using these methods through simulation study. The new method gives similar results under the normal situation and much better results when the data has outliers.