H.M. Barakat

Exact prediction intervals for future exponential lifetime based on random generalized order statistics

In this paper we develop two pivotal quantities to construct exact predication intervals for future exponential lifetime based on a random number of lower generalized order statistics. The distribution functions of the two pivotal quantities, when the sample size is assumed to be integer-valued random variable, are derived. Three important special cases for the random sample size are presented. A simulation study is conducted for illustrative purposes.

Original article: Prediction intervals of future observations for a sample of random size from any continuous distribution

In this paper, a general method for predicting future observations from any arbitrary continuous distribution is proposed. Two pivotal statistics are developed to construct prediction intervals of future observations in two cases. In the first case, we assume fixed sample size, while in the second case, the sample size is assumed to be positive integer-valued random variable independent of the observations. Explicit forms for the distribution functions of the pivotal statistics are derived. Some special cases for the random sample size are considered. An algorithm is constructed to demonstrate the practical importance of the theoretical results. Moreover, simulation study is applied on some important distributions to investigate the efficiency of the suggested method. Finally, an example for real lifetime data is analyzed, where it is assumed that the distribution of the data is unknown.

On the confidence region for the bivariate co-ordinate-wise quantiles of the continuous bivariate distribution functions

In this paper, the distribution-free confidence region (rectangular) for the vector of the co-ordinate-wise quantiles of a general continuous bivariate distribution function is explicitly derived. This confidence region, in general, depends on the dependence function. A procedure is suggested which enables one to attach a confidence coefficient to the estimate of the confidence region even if the dependence function is unknown. Moreover, some approximated distribution-free lower bounds, which are independent of the dependence function, of the confidence coefficient of this region are derived. Finally, some results of this study are extended to the three-dimensional vector of the co-ordinate-wise quantiles.