Skew-normal revisited via some ranked set sampling schemes

Abstract

Ranked set sampling (RSS) was first introduced by McIntyre (1952) as a competitor of simple random sampling (SRS), the most common tool in the statistical methods. When the sample size is not large enough, it may be difficult to obtain a representative subset from the population based on SRS, but RSS and its generalizations overcome to this shortcoming. These sampling schemes usually work based on judgment ranking of the sample units. The present paper investigates the performance of the mentioned schemes when the underlying distribution is the well-known Azzalini’s skewnormal (SN) distribution. It also answers to an important question, that is, which kind of rank-based sampling methods is appropriate when the parent distribution is SN? To this end, the maximum (penalized) likelihood estimation as well as the method of moments are 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 Pitman measure of closeness criteria through a simulation study. Results show that the suggested scheme is highly dependent on the sign of the skewness parameter.