Prediction for the Future Record Values from Logistic Distribution

by Labiba Hasab El-Naby .

Abstract: In this paper, we deal with some point and interval prediction methods for future record values. In particular, having observed a sequence of record values from logistic distribution, we consider maximum likelihood predictor (MLP), best linear unbiased predictor (BLUP), and median unbiased predictor (MUP). The predictive likelihood equations cannot be solved to obtain closed form for the MLP. Either BLUP or MUP has explicit form and is quite easy to compute. Monte Carlo simulations were performed to estimate MSEs of these predictors. It is shown that efficiency of MUP relative to BLUP is high for most values of m and n considered in this paper. Some approaches are proposed for constructing prediction interval for the future record values. These approaches depend on location and scale invariant statistics, pivotal quantity and conditional distribution of (Xu(n) Xu(m)) given Xu(m),n ? m. We have determined some percentage points of the statistics considered in this paper through Monte Carlo simulations (based on 10,000 runs). With the help of these points, one could easily construct 100(1- ?)% prediction intervals for the future record value. A comparison among prediction intervals for future record values is made via extensive Monte Carlo simulations. In most simulation cases the prediction interval based on conditional distribution of (Xu(n) Xu(m)) given Xu(m) is superior in terms of larger estimated coverage probabilities and shorter estimated average lengths.

Key Words: Logistic distribution; Upper record values; Point prediction; Interval prediction; Maximum likelihood predictor; Best linear unbiased predictor; Median unbiased predictor; Location-scale invariant statistic; Monte Carlo simulation

Labiba Hasab El-Naby ,

Editor: Ashour, S. Kamel,

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