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Motivated mainly by lifetime issues, a new lifetime distribution coined ``Discrete Poisson-Gold distribution'' is introduced in this paper. Different structural properties of the new distribution are derived including moment generating function and the $r^{th}$ moment and others are presented. In addition, we discussed various important mathematical properties of the new distribution including estimation procedures for estimating the distribution parameters using the maximum likelihood and method of moments. The usefulness and credibility of the distribution are illustrated by means of two real-data applications to show its superior performance over some other well-known lifetime distributions and to prove its versatility in practical applications.

The classical maximum likelihood estimation fails to estimate the simple linear measurement error model, with or without equation error, unless additional assumptions are made about the structural parameters. In the literature there are six different assumptions that could be added in order to solve the measurement error models. In this paper, we proposed an entropy-type estimator based on the generalized maximum entropy estimation approach, which allows one to abstract away from the additional assumptions that are made in the classical method. Monte Carlo experiments were carried out in order to investigate the performance of the proposed estimators. The simulation results showed that the entropy-type estimator of unknown parameters has outperformed the classical estimators in terms of mean square error criterion.

In this paper an estimation method based on double phase sampling is proposed to improve the efficiency of estimating the population mean. An extension is presented for the bivariate case to estimate the parameters of the simple linear regression model. Conclusions of this study show that using the proposed method with symmetric populations, the estimator of the population mean is unbiased and more efficient than the traditional one that is based on a simple random sample. Results for the standard uniform and the exponential distribution are given. Simulation results show that the proposed method is also more efficient than the traditional one in case of estimating the regression parameters. An application to a real data set is also given.