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Consider a two-sampling scheme in which an initial sample is first taken from the underlying population and then by assuming a suitable restriction on this sample, some more data points are observed as a new restricted sample. This sampling scheme is used to do inference about the lower quantiles of the underlying distribution. The results are compared with those of simple random sampling in view of mean squared error and Pitman’s measure of closeness criteria for exponential and uniform distributions. It will be shown that the proposed sampling scheme would improve the performance of the point estimators of the lower quantiles of the population. [ABSTRACT FROM PUBLISHER]

Consider k independent random samples with different sample sizes such that the ith sample comes from the cumulative distribution function (cdf) Fi = 1 - (1 - F)αi, where αi 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. [ABSTRACT FROM AUTHOR]

Two sampling designs via inverse sampling for generating record data and their concomitants are considered: single sample and multisample. The purpose here is to compare the Fisher information in these two sampling schemes. It is shown that the comparison criterion depends on the underlying distribution. Several general results are established for some parametric families and their well known subclasses such as location-scale and shape families, exponential family and proportional (reversed) hazard model. Farlie-Gumbel-Morgenstern (FGM) family, bivariate normal distribution, and some other common bivariate distributions are considered as examples for illustrations and are classified according to this criterion. [ABSTRACT FROM AUTHOR]

Let Xi,j (1 ≤ i ≤ k, 1 ≤ j ≤ ni) be independent random variables and for a fixed i, Xi,j's, (1 ≤ j ≤ ni) be identically distributed random variables with survival function [image omitted], where αi is a known positive constant. Also, suppose Mi and M'i, respectively, denote the maximum and minimum of the ith sample. This article investigates the nonparametric confidence intervals for an arbitrary quantile of the distribution F and tolerance limits based on these statistics. Various cases have been studied and in each case, the nonparametric confidence intervals are obtained and exact expressions for the confidence coefficients of these confidence intervals are derived. A data set representing the time of successive failures of the air conditioning system on Boeing 720 jet aircraft is used to illustrate the results. Finally, the accuracy of the proposed procedure has been investigated, when αi's are unknown via a simulation study. [ABSTRACT FROM AUTHOR]