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In this paper, the discrete extended Weibull distribution is introduced by discretizing a new extended the continuous Weibull distribution. The new model has decreasing, increasing, constant and upside-down bathtub shaped hazard rates. Some of basic distributional and reliability properties are studied. The maximum likelihood method is used to estimate the parameters of the model. The performance of the estimation method is evaluated by a Monte-Carlo simulation. Four-real life data sets are considered for illustrating the advantages of the proposed distribution over some other well-known discrete distributions.INDEX TERMS Discrete extended Weibull distribution, hazard rate, estimation method.

In sample surveys, it is usual to make use of auxiliary information to increase the precision of estimators. We propose a new exponential ratio-type estimator of a finite population mean using linear combination of two auxiliary variables and obtain mean square error (MSE) equation for proposed estimator. We find theoretical conditions that make proposed estimator more efficient than traditional multivariate ratio estimator using information of two auxiliary variables, the estimator of Bahl and Tuteja and the estimator proposed by Abu-Dayeh et al. In addition, we support these theoretical results with the aid of two numerical examples.