Problem statement: In this study, the researcher considers the problem of estimation of the mean of the truncated exponential distribution. Approach: This study contracted with maximum likelihood and unique minimum variance unbiased estimators and gives a modification for the maximum likelihood estimator, asymptotic variances and asymptotic confidence intervals for the estimators. The properties of these estimators in small, moderate and large samples were investigated via asymptotic theory and computer simulation. Results: It turns out that the modified maximum likelihood estimator was more efficient than the others and exists with probability 1. Conclusion: The modified maximum likelihood estimator was always exist, fast and straightforward to compute and more likely to yield feasible values than the unique minimum variance unbiased estimator. Its variance was well approximated by the large sample variance of the other estimators.

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The paper deals with constructing a model for Bayesian sampling plans for the system "Average out going quality level ()", where the percentage of defectives is varied fro m lot to lot, so it considered to be a rando m variable, having a prior d istribution (), wh ich must be fitted to represent the distribution of percentage of defectives efficiently. The parameters of this distribution must estimated, and then used in model construction. The aim of the model is to find the parameters of single Bayesian sampling plan (,), the sample size, and the acceptance number (), fro m minimizing the total cost of the model, which co mprises cost inspection and cost of repairing or replacement of defective units. In addition to cost of rejecting goo items, which is a penalty cost. Also the construction depend on decision rule[ ()], for acceptance and decision rule for rejection[1 − ()]. Finally the build model can be applied to another distribution like Gamma-Poisson, Normal-Beta, to find the sampling plan (,) necessary to test the product of the lot and to have a production with accepted () to satisfy consumer's and producer's risk. All the derivation required to build this cost function are exp lained and all the results of obtained samples and applications are illustrated in tables.

Problem statement: The double Pareto distribution appeared most often as model for variety of fields, including archaeology, biology, economics, environmental science, finance and physics. The distribution exhibits Paretian power-law behavior in both tails. The family of double Pareto distributions has recently been proposed for modeling growth rates such as annual gross domestic product, stock prices, foreign currency exchange rates and company sizes. In this study, I develop parameter estimates for the double Pareto distribution that are easy to compute. I compare the performance of the maximum likelihood estimate with Bayesian and the method of moments estimates. Approach: This study contracted with maximum likelihood, the method of moments and Bayesian using Jeffrey’s prior and the extension of Jeffrey’s prior information. The comparisons are made on the performance of these estimators with respect to the Mean Squared Error (MSE) for small, moderate and large samples and for some values of the scale and the extension of Jeffrey’s prior parameters using the simulation techniques. Results: It turns out that the maximum likelihood method and Bayesian method with Jeffrey’s prior result in smaller MSE compared to others in all cases. Conclusion: Based on the results of the simulation, the maximum likelihood method and Bayesian method with Jeffrey’s prior are found to be the best with respect to MSE