On distribution selection under ranked set sampling schemes

Distribution selection plays a key role in parametric statistics. Choosing one from a set of candidate distributions that best fits the sample data is a recurring task in a large number of statistical analysis. The choice of a misspecified and/or poor fitted distribution can lead to unreliable results and conclusions. Although distribution selection has been widely studied regarding goodness of fit procedures, less attention has been given on how the sampling design impacts the chance of choosing the most suitable distribution. In this work we address the performance of ranked set sampling (RSS), extreme ranked set sampling (ERSS), and mixture ranked set sampling (MRSS) in distribution selection. In particular, we focus on count data, an important and very usual class of random variables. A comprehensive simulation study was carried out, accounting for five distributions: Poisson, negative binomial, geometric, zero-inflated Poisson, and zero-inflated negative binomial. Results show that RSS and extensions performed better than simple random sampling (SRS) under perfect ranking. When ranking errors are present, better efficiency depends on how accurate is the ranking criterion, and the different RSS-based designs also differ in terms of their robustness. Findings are reinforced by additional simulation based on two real data sets.