Tests of normality based on EDF statistics using partially rank ordered set sampling designs

Authors : Yusuf Can SEVİL, Tuğba YILDIZ

Pages : 52-73

View : 24 | Download : 9

Publication Date : 2021-07-01

Article Type : Research Paper

Abstract :In this study, we considered five goodness-of-fit insert ignore into journalissuearticles values(GOF); tests based on empirical distribution function insert ignore into journalissuearticles values(EDF); which are Kolmogorov-Smirnov insert ignore into journalissuearticles values(D);, Kuiper insert ignore into journalissuearticles values(V );, Cram´er-von Mises insert ignore into journalissuearticles values(W2);, Watson insert ignore into journalissuearticles values(U2);, Anderson-Darling insert ignore into journalissuearticles values(A2); tests to assess normality. Thus, we first suggested the EDFs based partially rank ordered set insert ignore into journalissuearticles values(PROS); sampling designs which are known as PROS Level-0, Level-1 and Level-2 sampling designs. Then, we discussed the relative efficiencies of the suggested EDFs w.r.t their counterparts of simple random sampling insert ignore into journalissuearticles values(SRS); and ranked set sampling insert ignore into journalissuearticles values(RSS);. The main idea of this study is to compare the performances of the five different GOF tests based on PROS sampling designs with the GOF tests based on SRS and RSS. For this purpose, we investigated the power of the suggested GOF tests based on PROS sampling designs by performing simulations. In addition to the simulations, a real data set is considered to illustrate the GOF tests based on PROS sampling designs. According to the results, it can be seen that the EDFs based on PROS sampling designs are more efficient than the EDFs based on SRS and RSS. Also, it is clearly appeared that the GOF tests, Kolmogorov-Smirnov insert ignore into journalissuearticles values(D);, Cram´er-von Mises insert ignore into journalissuearticles values(W2); and Anderson- Darling insert ignore into journalissuearticles values(A2);, based on PROS sampling designs has the best power performance.
Keywords : Ranked set sampling, Partially rank ordered set, Sampling designs, Empirical distribution function, Type I error, Goodness of fit tests, Power of test