Browsing by Author "Aldallal R.A."

Filter results by typing the first few letters
Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Current records and record range with some applications
    (Korean Statistical Society, 2014) Barakat H.M.; Nigm E.M.; Aldallal R.A.; Department of Mathematics; Faculty of Science; Zagazig University; Zagazig; Egypt; Department of Mathematics and Statistics; MSA University; Cairo; Egypt
    In a sequence of independent and identically distributed (iid) random variables, the upper (lower) current records and record range are studied. We derive general recurrence relations between the single and product moments for the upper and lower current records based on Weibull and positive Weibull distributions, as well as Pareto and negative Pareto distributions, respectively. Moreover, some asymptotic results for general current records are established. In addition, a recurrence relation and an explicit formula for the moments of record range based on the exponential distribution are given. Finally, numerical examples are presented to illustrate and corroborate theoretical results. � 2013 The Korean Statistical Society.
  • Thumbnail Image
    Item
    Exact prediction intervals for future current records and record range from any continuous distribution
    (Institut d'Estadistica de Catalunya, 2014) Barakat H.M.; Nigm E.M.; Aldallal R.A.; Department of Mathematics; Faculty of Science; Zagazig University; Zagazig; Egypt; Department of Mathematics and Statistics; MSA University; Cairo; Egypt
    In this paper, a general method for predicting future lower and upper current records and record range from any arbitrary continuous distribution is proposed. Two pivotal statistics with the same explicit distribution for lower and upper current records are developed to construct prediction intervals for future current records. In addition, prediction intervals for future observations of the record range are constructed. A simulation study is applied on normal and Weibull distributions to investigate the efficiency of the suggested method. Finally, an example for real lifetime data with unknown distribution is analysed.