چکیده:
In many experiments, such as biology and quality control problems, sample size cannot always be considered as a constant value. Therefore, the problem of predicting future data when the sample size is an integer-valued random variable can be an important issue. This paper describes the prediction problem of future order statistics based on upper and lower records. Two different cases for the size of the future sample is considered as fixed and random cases. To do this, we first derive a general formula for the coverage probability of the prediction interval for each case. For the case that the sample size is a random variable, we consider two different distributions for the sample size, such as binomial and Poisson distributions and we study further details. The numerical computations are also given in this paper. Another purpose of this paper is to determine the optimal prediction interval for each case. Finally, the application of the proposed prediction interval is illustrated by analyzing the data in a real-world case study.
خلاصه ماشینی:
"Optimal Non-Parametric Prediction Intervals for Order Statistics with Random Sample Size Elham Basiri1*, Aylin Pakzad 2 1.
This paper describes the prediction problem of future order statistics based on upper and lower records.
Recently, Basiri and Ahmadi (2015) considered two sample prediction problems for generalized order statistics when the size is random.
In this paper, we investigate nonparametric predicting future order statistics based on observed records, assuming the size of the future sample as a random variable.
The rest of this paper is set as follows: In Section 2, a general formula for the coverage probability of prediction intervals for future order statistics based on observed upper and lower records is derived.
Section 3 is concerned with finding optimal prediction intervals for future random order statistics based on upper and lower records in the both cases of random and fixed samples.
Prediction of Order Statistics In this section, let X i:N be the i-th order statistic from a future X - By considering upper and lower records jointly, Ahmadi and Balakrishnan (2010) showed that ( R L , RU ), r, s ³ 1, is a predictionr s interval for X i:N , with coverage probability given by and (6), respectively.
Construction of prediction intervals for future order statistics with random sample size based on upper records is stated in the following theorem.
Prediction intervals for future records and order statistics coming from two parameter exponential distribution.
Prediction intervals for generalized- order statistics with random sample size."