inverse sampling design is generally considered to be appropriate technique when the population is divided into two subpopulations, one of which contains only few units. in this paper, we derive the horvitz-thompson estimator for the population mean under inverse sampling designs, where subpopulation sizes are known. we then introduce an alternative unbiased estimator, corresponding to post-str...

In practice, we often encounter situations where a sample size is not defined in advance and can be random value. The randomness of the crucially changes asymptotic properties underlying statistic. present paper second order Chebyshev--Edgeworth Cornish--Fisher expansions based Student's $t$- Laplace distributions their quantiles are derived for median with special kind.

A simulation study is designed to explore accuracy and precision of parameter estimation of cognitive attributes using the crossed random effects linear logistic test model (CRELLTM) with PROC GLIMMIX. The CRELLTM characterizes the weight of the cognitive attributes for item difficulties as random coefficients. The SAS® GLIMMIX package is applied to obtain parameter estimates. A series of simul...

An important problem in multilevel modeling is what constitutes a sufficient sample size for accurate estimation. In multilevel analysis, the major restriction is often the higher-level sample size. In this paper, a simulation study is used to determine the influence of different sample sizes at the group level on the accuracy of the estimates (regression coefficients and variances) and their s...

A one-way randomeffectsmodel is consideredfor the log-transformedshift-longpersonal exposure measurements, where the random effect in the model represents an effect due to the worker. Following a previousapproach,we address a hypothesis-testingproblem involving the proportionof workers for whom the mean exposure exceeds the occupational exposure limit. A conŽ dence interval is constructed for t...

Analogous to the Donsker theorem on partial cumulative sums of independent random variables, for one-sample rank-order statistics, weak convergence to Brownian motion processes is studied here. This yields a simple proof of the asymptotic normality of the related rank statistics for random sample sizes. Analogous to the Donsker theorem on partial cumulative sums of independent random variables,...