Quartile ranked set sampling for estimating the distribution function

Quartile ranked set sampling (QRSS) method is suggested by Muttlak (2003) for estimating the population mean. In this article, the QRSS procedure is considered to estimate the distribution function of a random variable. The proposed QRSS estimator is compared with its counterparts based on simple random sampling (SRS) and ranked set sampling (RSS) schemes. It is found that the suggested estimator of the distribution function of a random variable X for a given x is biased and more efficient than its competitors using SRS and RSS.