Reconstructing past fractional record values | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 24, Issue 4, 2016, Pages 622-628 PDF (408.79 K) | ||
| DOI: 10.1016/j.joems.2016.04.002 | ||
| Authors | ||
| Magdy E. El-Adll; Amany E. Aly | ||
| Department of Mathematics, Faculty of Science, Helwan University, Ain Helwan, Cairo, Egypt | ||
| Abstract | ||
| In this paper, reconstructing past fractional upper (lower) records from any absolutely continuous distribution is proposed. For this purpose, two pivotal quantities are given and their exact distributions are derived. More detailed results, including the case of unknown parameters, are given for the exponential and Fr ´e chet distributions. Moreover, the exact mean square reconstructor errors are obtained and some comparisons between the pivotal quantities are performed. To explore the efficiency of the obtained results, a simulation study is conducted and two real data sets are analyzed | ||
| Keywords | ||
| Fractional records; pivotal quantity; reconstruction interval; coverage probability; Monte Carlo simulation | ||
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