SKEW-NORMAL REVISITED VIA SOME RANKED SET SAMPLINGSCHEMES

Özet

Abstract.Ranked set sampling (RSS) was first introduced by McIntyre (1952) as acompetitor of simple random sampling (SRS), the most common tool in the statisticalmethods. When the sample size is not large enough, it may be difficult to obtain arepresentative subset from the population based on SRS, but RSS and its generalizationsovercome to this shortcoming. These sampling schemes usually work based on judgmentranking of the sample units. The present paper investigates the performance of thementioned schemes when the underlying distribution is the well-known Azzalini’s skew-normal (SN) distribution. It also answers to an important question, that is, which kind ofrank-based sampling methods is appropriate when the parent distribution is SN? To thisend, the maximum (penalized) likelihood estimation as well as the method of momentsare applied as the estimation approaches of the skewness parameter of SN distribution.Comparison of the estimators is carried out via their mean squared error and the Pitmanmeasure of closeness criteria through a simulation study. Results show that the suggestedscheme is highly dependent on the sign of the skewness parameter.