Parameter Estimation for the Power Generalized Weibull Distribution Based on One- and Two-Stage Ranked Set Sampling Designs

Parameter estimation Based on Double Ranked Set Sampling (DRSS) designs was recently developed by Sabry et al., (2019) and shows high efficiency and precision of the likelihood estimators when applied to the two-parameter Weibull distribution. In this paper the likelihood function of the General Double Ranked Set Sampling (GDRSS) design discussed by Taconeli & Cabral (2019) is derived and the two double ranked set sampling designs DRSS and GDRSS are compared along with the usual Ranked Set Sampling (RSS) and Extreme Ranked Set Sampling (ERSS) designs for the estimation of the parameters of the Power Generalized Weibull (PGW) distribution which is an extension of the two parameter Weibull distribution. An intensive simulation has been made to compare the one- and the two- stages designs. The results show that likelihood estimation based on DRSS and GDRSS designs provide more efficient estimators than the usual RSS and ERSS designs. Moreover, the GDRSS is slightly more efficient that the DRSS designs in the case of estimating the PGW distribution