15 Prediction of order statistics

Based on record statistics from Lindley distribution, we consider here the problem of estimating the model parameter and predicting the unobserved records. Frequentist and Bayesian analyses are discussed for making some inferences for the model parameter and prediction of unobserved records. Frequentist methods involving maximum likelihood estimation and moments based estimation and Bayesian sampling-based technique are applied for estimating the unknown shape parameter as well as predicting the future unobserved units. The corresponding point predictors and credible intervals of future record values based on an informative set of records can be developed. Real data analysis has been performed for illustrative purposes.

show abstract

“…See, for example, Kaminsky and Nelson (1998). In this section, we consider the problem of predicting the future records from LI distribution.…”

Section: Bayesian Sample-based Predictionmentioning

confidence: 99%

Statistical inference based on Lindley record data

et al. 2016

View full text Add to dashboard Cite

show abstract

“…Prediction of unobserved data is important especially in actuarial, medical and engineering sciences. Balakrishnan and Rao (1997) and Kaminsky and Nelson (1998). The rest of this paper is prepared as follows: In section 2, we estimate the MLEs for both the scale and the location parameters of the Rayleigh distribution.…”

Section: Introductionmentioning

confidence: 99%

Statistical Inferences of the Rest Lifetimes of Ball Bearings' Residual Lifetimes Based on Rayleigh Residual Type II Censored Data

Abufoudeh¹,

Bdair²,

Awwad³

2016

Journal of Mathematics and Statistics

View full text Add to dashboard Cite

Abstract:In this study, we consider statistical inference problems for the residual life data that come from the Rayleigh model based on type II censored data. Maximum likelihood and Bayesian approaches are used to estimate the scale and location parameters for the Rayleigh model, the Gibbs sampling procedure is used to draw Markov Chain Monte Carlo (MCMC) samples and MCMC samples have been used to compute the Bayes estimates and to construct symmetric credible intervals. Furthermore, we estimate the posterior predictive density of the future ordered data and then obtain the corresponding predictors. The Gibbs and Metropolis samplers are used to predict the life lengths of the missing lifetimes in multiple stages of the residual type II censored sample. Numerical comparisons for a real life data involving the ball bearings' lifetimes and the artificial data are conducted to assess the performance of the parameters' estimators and the predictors of future ordered data using some specialized computer programs.

show abstract

“…Hsieh (1997) studied the construction of prediction intervals for future Weibull order statistics for two cases: when only previous independent failure data are available, and when both previous independent failure data and early failure data in current experiment are available. Kaminsky and Nelson (1998) considered the prediction of order statistics in one-sample as well as two-sample cases, and obtained linear point predictors and prediction intervals based on samples from location-scale families. Raqab and Balakrishnan (2008) obtained distribution-free prediction intervals for records from the Y -sequence based on record values from the X -sequence of iid random variables from the same distribution.…”

Section: Introductionmentioning

confidence: 99%

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

Ahmadi

2011

Journal of the Korean Statistical Society

View full text Add to dashboard Cite

a b s t r a c tIn 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.

show abstract

15 Prediction of order statistics

Cited by 53 publications

References 29 publications

Statistical inference based on Lindley record data

Statistical inference based on Lindley record data

Statistical Inferences of the Rest Lifetimes of Ball Bearings' Residual Lifetimes Based on Rayleigh Residual Type II Censored Data

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

Contact Info

Product

Resources

About

15 Prediction of order statistics

Cited by 53 publications

References 29 publications

Statistical inference based on Lindley record data

Statistical inference based on Lindley record data

Statistical Inferences of the Rest Lifetimes of Ball Bearings&#039; Residual Lifetimes Based on Rayleigh Residual Type II Censored Data

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

Contact Info

Product

Resources

About

Statistical Inferences of the Rest Lifetimes of Ball Bearings' Residual Lifetimes Based on Rayleigh Residual Type II Censored Data