PARAMETRIC DISTRIBUTIONS OF COMPLEX SURVEY DATA UNDER INFORMATIVE PROBABILITY-SAMPLING

The sample distribution is defined as the distribution of the sample m easurements given the selected sample. Under informative sampling, thi s distribution is different from the corresponding population distribu tion, although for several examples the two distributions are shown to be in the same family and only differ in some or all the parameters. A general approach of approximating the marginal sample distribution f or a given population distribution and first order sample selection pr obabilities is discussed and illustrated. Theoretical and simulation r esults indicate that under common sampling methods of selection with u nequal probabilities, when the population measurements are independent ly drawn from some distribution (superpopulation), the sample measurem ents are asymptotically independent as the population size increases; This asymptotic independence combined with the approximation of the ma rginal sample distribution permits the use of standard methods such as direct likelihood inference or residual analysis for inference on the population distribution.