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Abstract In this thesis we study, suggest and develop methods of prediction of future data. In particular, we concentrate on data based on mixture of two exponential distributions. The first aim of this work is developing several methods for constructing prediction intervals, or predictor points, for future observations based on pivotal statistics and some characterization properties of probability distributions. We suggest four pivotal statistics to get predictor points for the future observations. The new suggested methods, which are based on the characterization of probability distributions, will handle three different cases of predictions. The first case, when the sample size is enlarged, and then we seek to predict the new position of an observed item in the old random sample within the new random sample. The second case is just predicting future items, or set of future items, based on the observed ones, where in this case the sample size does not change. The third case is to consider the first and second cases when we assume that the sample size is a random variable (RV). The second aim of this work is to create a package in R to help users to apply these methods easily without exposure to mathematical equations. This thesis consists of five chapters. |