Prediction Intervals For Order Statistics Research Articles

Optimal Non-Parametric Prediction Intervals for Order Statistics with Random Sample Size

‎ 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.

Comparison among non parametric prediction intervals of order statistics

In this article, we are interested in conducting a comparison study between different non parametric prediction intervals of order statistics from a future sample based on an observed order statistics. Typically, coverage probabilities of well-known non parametric prediction intervals may not reach the preassigned probability levels. Moreover, prediction intervals for predicting future order statistics are no longer available in some cases. For this, we propose different methods involving random indices and fractional order statistics. In each case, we find the optimal prediction intervals. Numerical computations are presented to assess the performances of the so-obtained intervals. Finally, a real-life data set is presented and analyzed for illustrative purposes.

Bayesian prediction intervals of order statistics based on progressively type-II censored competing risks data from the half-logistic distribution

Abstract The competing risks model may be of great importance for an investigator in medical studies or in reliability analysis. In this article, Bayesian prediction bounds of order statistics based on progressively type-II censored competing risks data from a general class of distributions are obtained. The class of distributions includes, among others, Weibull, compound Weibull, Pareto, Gompertz, compound Gompertz and half-logistic distributions. The results are then applied to the half-logistic distribution. Based on three different progressive type-II censoring schemes, prediction intervals of the future order statistics are obtained. An illustrative example is presented to show the procedure. A Monte Carlo simulation study is performed and numerical computations are carried out to obtain the coverage probabilities and average interval lengths of the prediction intervals.

Prediction of order statistics and record values based on ordered ranked set sampling

In this paper, we consider two-sample prediction problems. First, based on ordered ranked set sampling (ORSS) introduced by Balakrishnan and Li [Ordered ranked set samples and applications to inference. Ann Inst Statist Math. 2006;58:757–777], we obtain prediction intervals for order statistics from a future sample and compare the results with the one based on the usual-order statistics. Next, we construct prediction intervals for record values from a future sequence based on ORSS and compare the results with the one based on an another independent record sequence developed recently by Ahmadi and Balakrishnan [Prediction of order statistics and record values from two independent sequences. Statistics. 2010;44:417–430].

Exact prediction intervals for order statistics from the Laplace distribution based on the maximum-likelihood estimators

In this work we construct exact prediction intervals for order statistics from the Laplace (double exponential) distribution. We consider both the one- and two-sample prediction cases. The intervals are based on certain pivotal quantities that employ the corresponding maximum-likelihood predictors and the predictive maximum-likelihood estimators of the unknown parameters. Similar to Iliopoulos and Balakrishnan [Exact likelihood inference for Laplace distribution based on Type-II censored samples. J. Statist. Plann. Inference. 2011;141:1224–1239], we express the distributions of the pivotal quantities as mixtures of ratios of linear combinations of independent standard exponential random variables. Since these distributions are in closed form we solve numerically the corresponding equations and obtain their exact quantiles. Tables containing selected quantiles of the pivotal quantities are provided. Numerical examples are also given for illustration purposes.

Two sample Bayesian prediction intervals for order statistics based on the inverse exponential-type distributions using right censored sample

Abstract In this paper, two sample Bayesian prediction intervals for order statistics (OS) are obtained. This prediction is based on a certain class of the inverse exponential-type distributions using a right censored sample. A general class of prior density functions is used and the predictive cumulative function is obtained in the two samples case. The class of the inverse exponential-type distributions includes several important distributions such the inverse Weibull distribution, the inverse Burr distribution, the loglogistic distribution, the inverse Pareto distribution and the inverse paralogistic distribution. Special cases of the inverse Weibull model such as the inverse exponential model and the inverse Rayleigh model are considered.

Distribution-free prediction intervals for order statistics based on record coverage

In this paper, based on the largest and smallest observations at the times when a new record of either kind (upper or lower) occurs, we discuss the prediction of future order statistics. The proposed prediction intervals are distribution-free in that the corresponding coverage probabilities are known exactly without any assumption about the parent distribution other than that it being continuous. An exact expression for the prediction coefficient of these intervals is derived. Similarly, prediction intervals for future records based on observed order statistics are also obtained. Finally, two real-life data, one involving the average July temperatures in Neurenburg, Switzerland, and the other involving the amount of annual rainfall at the Los Angeles Civic Center, are used to illustrate the procedures developed here.

Exact and adaptive prediction intervals for order statistics

We construct exact prediction intervals for future order statistics based on a random sample from a given family of distributions with unknown location and scale parameters. In the one sample problem, only a specified number of the first order statistics are available. In the two sample problem, predicitons are made for a second independent sample. We also propose an adaptive two stage procedure when the distribution is unknown. First the data are used to select a distribution and then a prediction interval for that distribution is constructed. We show that the adaptive procedure provides protection against model misspecification