Parameter Estimation of the Skew Normal Distribution Using a Double-Stage Ranked Set Sampling

Skew normal (SN) distribution plays an important role in modelling data with normal-like shape of the empirical distribution but with lack of symmetry (Azzalini, 1985). It has location, scale and shape parameters. The primary objective of this research is to estimate these parameters using a new approach of ranked set sampling (RSS) which we will call it a double stage RSS. The estimators obtained will be compared with those obtained by simple random sampling (SRS), RSS, and median RSS. The performance of the estimators will be evaluated by a simulation study. Finally, an illustrative example will be provided to show the efficiency of the new method in practice.