A New Morgenstern Type Bivariate Exponential Distribution with Known Coefficient of Variation by Ranked Set Sampling

Abstract

Cost-effective sampling methods are of major concern in some experiments, especially when the measurement of the characteristics is costly, painful, or time-consuming. The concept of ranked set sampling (RSS) was first introduced by McIntyre (1952) as a process of increasing the precision of sample mean as an unbiased estimator of population mean. The method of RSS provides an effective way to achieve observational economy or to achieve relatively more precision per unit of sampling. RSS as described by McIntyre (1952) is applicable whenever ranking of a set of sampling units can be done easily by judgment method. For a detailed discussion on theory and application of RSS, see Chen et al. (2004). In certain situations one may prefer exact measurements of some easily measurable variable X associated with the study variable Y to rank the units of samples rather than ranking them by a crude judgment method. Suppose the variable of interest Y, is difficult or much more expensive to measure, but an auxiliary variable X correlated with Y is readily measureable and can be ordered exactly. In this case as an alternative to McIntyre’s (1952) method of ranked set sampling, Stokes (1977) used an auxiliary variable for the ranking of sampling units.