Nonparametric Prediction Intervals for Future Order Statistics in a Proportional Hazard Model
Communication in Statistics- Theory and Methods (Impact Factor: 0.27). 05/2011; 40(10):1807-1820. DOI: 10.1080/03610921003714147
Consider k independent random samples with different sample sizes such that the ith sample comes from the cumulative distribution function (cdf) F i = 1 − (1 − F)α i , where α i is a known positive constant and F is an absolutely continuous cdf. Also, suppose that we have observed the maximum and minimum of the first k samples. This article shows how one can construct the nonparametric prediction intervals for the order statistics of the future samples on the basis of these information. Three schemes are studied and in each case exact expressions for the prediction coefficients of prediction intervals are derived. Numerical computations are given for illustrating the results. Also, a comparison study is done while the complete samples are available.
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- "For the last decade or so, there has been an overwhelming attention to PHR model, see Marshal and Olkin (2007) and also Ahmadi et al. (2009a, 2009b) who studied the problems of estimation and prediction for the PHR family based on k-record data. Razmkhah and Ahmadi (2011) constructed prediction intervals for future order statistics based on observed maxima and minima in a PHR model. Asgharzadeh and Valiollahi (2009) considered the estimation problem in respect of Bayesian and non-Bayesian approaches for the PHR family based on progressively Type-II censored samples. "
ABSTRACT: In this paper, we consider a sampling scheme in record-breaking data set up, as record ranked set sampling. We compare the proposed sampling with the well-known sampling scheme in record values known as inverse sampling scheme when the underlying distribution follows the proportional hazard rate (PHR) model. Various point estimators are obtained in each sampling schemes and compared with respect to mean squared error (MSE) and Pitman measure of closeness (PMC) criteria. It is observed in the most of situations, the new sampling scheme provides more efficient estimators than their counterparts. Finally, one data set has been analyzed for illustrative purposes.
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