Statistical inference for the unit compound Rayleigh model under ranked set sampling with application

Ranked set sampling (RSS) is especially effective when direct measurement of a variable is costly or time-consuming, but ranking the items on the basis of that variable is relatively simple and inexpensive. The unit compound Rayleigh (UCR) model is an effective method for capturing the properties of data sets that are affected by negatively skewed data. For the purpose of this study, a comprehensive comparison of several estimation methods is planned. These methods include maximum likelihood, Anderson–Darling, Cramer–von-Mises, maximum product of spacings, least squares, minimum spacing absolute distance, minimum spacing absolute-log distance, minimum spacing square distance, minimum spacing square-log distance, and minimum spacing Linex distance under RSS and SRS techniques. The results of the simulation demonstrate that the maximum product spacing and maximum likelihood estimation methods are preferable to alternative approaches when evaluating the quality of RSS and SRS estimates, respectively. In addition, the findings highlight the efficiency advantages of RSS over SRS, as evidenced by improved accuracy metrics. The practical importance of our findings is demonstrated by a practical application involving the survival time of 72 guinea pigs infected with the virulent tuberculosis bacillus.