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Omer Ozturk - One of the best experts on this subject based on the ideXlab platform.
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quantile inference based on partially rank ordered Set Samples
Journal of Statistical Planning and Inference, 2012Co-Authors: Omer OzturkAbstract:Abstract This paper develops statistical inference for population quantiles based on a partially rank-ordered Set (PROS) Sample design. A PROS Sample design is similar to a Ranked Set Sample with some clear differences. This design first creates partially rank-ordered subSets by allowing ties whenever the units in a Set cannot be Ranked with high confidence. It then selects a unit for full measurement at random from one of these partially rank-ordered subSets. The paper develops a point estimator, confidence interval and hypothesis testing procedure for the population quantile of order p. Exact, as well as asymptotic, distribution of the test statistic is derived. It is shown that the null distribution of the test statistic is distribution-free, and statistical inference is reasonably robust against possible ranking errors in ranking process.
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exact two Sample nonparametric test for quantile difference between two populations based on Ranked Set Samples
Annals of the Institute of Statistical Mathematics, 2009Co-Authors: Omer Ozturk, N BalakrishnanAbstract:Creation of a Ranked Set Sample, by its nature, involves judgment ranking error within Set units. This ranking error usually distorts statistical inference of the population characteristics. Tests may have inflated sizes, confidence intervals may have incorrect coverage probabilities, and the estimators may become biased. In this paper, we develop an exact two-Sample nonparametric test for quantile shift between two populations based on Ranked Set Samples. This test is based on two independent exact confidence intervals for the quantile of interest corresponding to the two populations and rejects the null hypothesis of equal quantiles if these intervals are disjoint. It is shown that a pair of 83 and 93% confidence intervals provide a 5 and 1% test for the equality of quantiles. The proposed test is calibrated for the effect of judgment ranking error so that the test has the correct size even under a wide range of judgment ranking errors. A small scale simulation study suggests that the test performs quite well for cycle sizes as small as 2.
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statistical inference under a stochastic ordering constraint in Ranked Set sampling
Journal of Nonparametric Statistics, 2007Co-Authors: Omer OzturkAbstract:This paper introduces estimators for the judgment class and population cumulative distribution functions (CDF) under stochastic order restriction. The estimators are defined as the minimizer of a version of the Cramer-von Mises distance function. It is shown that the new estimators are strongly and uniformly consistent for the judgment class population distributions and have smaller integrated mean square errors than the integrated mean square errors of the empirical CDF estimators. The proposed estimators are used to calibrate the effect of imperfect ranking on statistical procedures. It is shown that this calibration works quite well in Ranked Set Sample Mann–Whitney–Wilcoxon rank-sum and sign tests. The use of estimators and calibration procedure are illustrated on a Ranked Set Sample data.
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Ranked Set Sample nonparametric quantile confidence intervals
Journal of Statistical Planning and Inference, 2006Co-Authors: Omer Ozturk, Jayant V DeshpandeAbstract:A nonparametric exact quantile interval is developed for Ranked-Set Samples. The proposed interval provides higher coverage probability and shorter expected length than its simple random Sample analog. In order to achieve the desired confidence level a distribution-free confidence interval that interpolates the adjacent order statistics is constructed.
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estimation of population mean and variance in flock management a Ranked Set sampling approach in a finite population Setting
Journal of Statistical Computation and Simulation, 2005Co-Authors: Omer Ozturk, Omer Cevdet Bilgin, Douglas A WolfeAbstract:Ranked Set sampling is a sampling technique that provides substantial cost efficiency in experiments where a quick, inexpensive ranking procedure is available to rank the units prior to formal, expensive and precise measurements. Although the theoretical properties and relative efficiencies of this approach with respect to simple random sampling have been extensively studied in the literature for the infinite population Setting, the use of Ranked Set sampling methods has not yet been explored widely for finite populations. The purpose of this study is to use sheep population data from the Research Farm at Ataturk University, Erzurum, Turkey, to demonstrate the practical benefits of Ranked Set sampling procedures relative to the more commonly used simple random sampling estimation of the population mean and variance in a finite population. It is shown that the Ranked Set Sample mean remains unbiased for the population mean as is the case for the infinite population, but the variance estimators are unbiased...
Mohammad Z Raqab - One of the best experts on this subject based on the ideXlab platform.
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inference for a simple step stress model based on ordered Ranked Set sampling
Applied Mathematical Modelling, 2019Co-Authors: Mohammad Z Raqab, Mohammed S KotbAbstract:Abstract In this paper, we considered the inference problem on simple step-stress accelerated life test data from one-parameter exponential distribution under type-I censored ordered Ranked Set Sample with cumulative exposure model. The Bayesian estimators and credible intervals for the model parameters are developed and compared with the corresponding estimators based on simple random sampling. Two real data Sets and numerical simulation evaluations are presented to illustrate all the results developed here. The simulation study indicated that the proposed Bayes estimators and credible intervals based on ordered Ranked Set sampling performed better than their counterparts using simple random sampling.
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bayesian inference and prediction of the rayleigh distribution based on ordered Ranked Set sampling
Communications in Statistics - Simulation and Computation, 2018Co-Authors: Mohammed S Kotb, Mohammad Z RaqabAbstract:ABSTRACTBased on ordered Ranked Set Sample, Bayesian estimation of the model parameter as well as prediction of the unobserved data from Rayleigh distribution are studied. The Bayes estimates of the parameter involved are obtained using both squared error and asymmetric loss functions. The Bayesian prediction approach is considered for predicting the unobserved lifetimes based on a two-Sample prediction problem. A real life dataSet and simulation study are used to illustrate our procedures.
Mohammed S Kotb - One of the best experts on this subject based on the ideXlab platform.
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inference for a simple step stress model based on ordered Ranked Set sampling
Applied Mathematical Modelling, 2019Co-Authors: Mohammad Z Raqab, Mohammed S KotbAbstract:Abstract In this paper, we considered the inference problem on simple step-stress accelerated life test data from one-parameter exponential distribution under type-I censored ordered Ranked Set Sample with cumulative exposure model. The Bayesian estimators and credible intervals for the model parameters are developed and compared with the corresponding estimators based on simple random sampling. Two real data Sets and numerical simulation evaluations are presented to illustrate all the results developed here. The simulation study indicated that the proposed Bayes estimators and credible intervals based on ordered Ranked Set sampling performed better than their counterparts using simple random sampling.
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bayesian inference and prediction of the rayleigh distribution based on ordered Ranked Set sampling
Communications in Statistics - Simulation and Computation, 2018Co-Authors: Mohammed S Kotb, Mohammad Z RaqabAbstract:ABSTRACTBased on ordered Ranked Set Sample, Bayesian estimation of the model parameter as well as prediction of the unobserved data from Rayleigh distribution are studied. The Bayes estimates of the parameter involved are obtained using both squared error and asymmetric loss functions. The Bayesian prediction approach is considered for predicting the unobserved lifetimes based on a two-Sample prediction problem. A real life dataSet and simulation study are used to illustrate our procedures.
N Balakrishnan - One of the best experts on this subject based on the ideXlab platform.
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exact two Sample nonparametric test for quantile difference between two populations based on Ranked Set Samples
Annals of the Institute of Statistical Mathematics, 2009Co-Authors: Omer Ozturk, N BalakrishnanAbstract:Creation of a Ranked Set Sample, by its nature, involves judgment ranking error within Set units. This ranking error usually distorts statistical inference of the population characteristics. Tests may have inflated sizes, confidence intervals may have incorrect coverage probabilities, and the estimators may become biased. In this paper, we develop an exact two-Sample nonparametric test for quantile shift between two populations based on Ranked Set Samples. This test is based on two independent exact confidence intervals for the quantile of interest corresponding to the two populations and rejects the null hypothesis of equal quantiles if these intervals are disjoint. It is shown that a pair of 83 and 93% confidence intervals provide a 5 and 1% test for the equality of quantiles. The proposed test is calibrated for the effect of judgment ranking error so that the test has the correct size even under a wide range of judgment ranking errors. A small scale simulation study suggests that the test performs quite well for cycle sizes as small as 2.
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some simple nonparametric methods to test for perfect ranking in Ranked Set sampling
Journal of Statistical Planning and Inference, 2008Co-Authors: N BalakrishnanAbstract:Abstract A lot of research on Ranked Set sampling (RSS) is based on the assumption that the ranking is perfect. Hence, it is necessary to develop some tests that could be used to validate this assumption of perfect ranking. In this paper, we introduce some simple nonparametric methods for this purpose. We specifically define three test statistics, N k , S k and A k , based on one-cycle RSS, which are all associated with the ordered Ranked Set Sample (ORSS). We then derive the exact null distributions and exact power functions of all these tests. Next, by using the sum or the maximum of each statistic over all cycles, we propose six test statistics for the case of multi-cycle RSS. We compare the performance of all these tests with that of the Kolmogorov–Smirnov test statistic proposed earlier by Stokes and Sager [1988. Characterization of a Ranked-Set Sample with application to estimating distribution functions. J. Amer. Statist. Assoc. 83, 35–42] and display that all proposed test statistics are more powerful. Finally, we present an example to illustrate the test procedures discussed here.
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blues of parameters of generalized geometric distribution using ordered Ranked Set sampling
Communications in Statistics - Simulation and Computation, 2005Co-Authors: N BalakrishnanAbstract:ABSTRACT As an alternative to the best linear unbiased estimates based on order statistics (BLUE-OS) for general location-scale distributions given by Lloyd (1952) and Downton (1954), Bhoj and Ahsanullah (1996) presented the best linear unbiased estimates based on Ranked Set Sample (BLUE-RSS) for the generalized geometric distribution. Hossain and Muttlak (2000) extended it to some other distributions, and gave the BLUE-RSS for the population mean and the standard deviation. Bhoj and Ahsanullah (1996) and Hossain and Muttlak (2000) arrived at the conclusion that the BLUE-RSS of the location parameter is more efficient than the BLUE-OS, while the BLUE-RSS of the scale parameter is not as efficient as the BLUE-OS for small n. In this article, we derive the best linear unbiased estimates using ordered Ranked Set sampling (BLUE-ORSS). These estimates are then compared with both BLUE-OS and BLUE-RSS for two special cases of the generalized geometric distribution. We show that BLUE-ORSS are uniformly better tha...
Douglas A Wolfe - One of the best experts on this subject based on the ideXlab platform.
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estimation of population mean and variance in flock management a Ranked Set sampling approach in a finite population Setting
Journal of Statistical Computation and Simulation, 2005Co-Authors: Omer Ozturk, Omer Cevdet Bilgin, Douglas A WolfeAbstract:Ranked Set sampling is a sampling technique that provides substantial cost efficiency in experiments where a quick, inexpensive ranking procedure is available to rank the units prior to formal, expensive and precise measurements. Although the theoretical properties and relative efficiencies of this approach with respect to simple random sampling have been extensively studied in the literature for the infinite population Setting, the use of Ranked Set sampling methods has not yet been explored widely for finite populations. The purpose of this study is to use sheep population data from the Research Farm at Ataturk University, Erzurum, Turkey, to demonstrate the practical benefits of Ranked Set sampling procedures relative to the more commonly used simple random sampling estimation of the population mean and variance in a finite population. It is shown that the Ranked Set Sample mean remains unbiased for the population mean as is the case for the infinite population, but the variance estimators are unbiased...
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a new Ranked Set Sample estimator of variance
Journal of The Royal Statistical Society Series B-statistical Methodology, 2002Co-Authors: Steven N Maceachern, Douglas A Wolfe, Omer Ozturk, Gregory V StarkAbstract:Summary. We develop an unbiased estimator of the variance of a population based on a Ranked Set Sample. We show that this new estimator is better than estimating the variance based on a simple random Sample and more efficient than the estimator based on a Ranked Set Sample proposed by Stokes. Also, a test to determine the effectiveness of the judgment ordering process is proposed.
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A new Ranked Set sampling protocol for the signed rank test
Journal of Statistical Planning and Inference, 2001Co-Authors: Omer Ozturk, Douglas A WolfeAbstract:Abstract In this paper, we construct a new Ranked Set sampling protocol that maximizes the Pitman asymptotic efficiency of the signed rank test. The new sampling design is a function of the Set size and independent order statistics. If the Set size is odd and the underlying distribution is symmetric and unimodal, then the new sampling protocol quantifies only the middle observation. On the other hand, if the Set size is even, the new sampling design quantifies the two middle observations. This data collection procedure for use in the signed rank test outperforms the data collection procedure in the standard Ranked Set Sample. We show that the exact null distribution of the signed rank statistic WRSS+ based on a data Set generated by the new Ranked Set Sample design for odd Set sizes is the same as the null distribution of the simple random Sample signed rank statistic WSRS+ based on the same number of measured observations. For even Set sizes, the exact null distribution of WRSS+ is simulated.
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optimal allocation procedure in Ranked Set sampling for unimodal and multi modal distributions
Environmental and Ecological Statistics, 2000Co-Authors: Mer Ztu O O Rk, Douglas A WolfeAbstract:This paper presents a Ranked Set Sample allocation procedure that is optimal for a number of nonparametric test procedures. We define a function that measures the amount of information provided by each observation given the actual joint ranking of all the units in a Set. The optimal Ranked Set Sample allocates order statistics by maximizing this information function. This paper shows that the optimal allocation of order statistics in a Ranked Set Sample is determined by the location of the mode(s) of the underlying distribution. For unimodal, symmetric distributions, optimal allocation always quantifies the middle observation(s). If the underlying distribution with cdf F is a multi-modal distribution with modes \(R, \ldots ,R_k \), then the optimal allocation procedure quantifies observations at \(mF(R_1 ), \ldots ,mF(R_1 )\) in a Set of size m. We provide similar results for unimodal, asymmetric distributions. We also propose a new sign test which considers the relative positions of the quantified observations from the same cycle in a Ranked Set Sample. The proposed sign test provides improvement in the Pitman efficiency over the Ranked Set Sample sign test of Hettmansperger (1995). It is shown that the information optimal allocation procedure induced by Pitman efficiency is equivalent to the optimal allocation procedure induced by the information criteria. We show that the finite Sample distribution of the proposed test based on this optimal design is binomial.
