On the Estimation of the Distribution Function Using Extreme and Median Ranked Set Sampling

We study relationships between extreme ranked set samples (ERSSs) and median ranked set sample (MRSS) with simple random sample (SRS). For a random variable X, we show that the distribution function estimator when using ERSSs and MRSS are more efficient than when using SRS and ranked set sampling for some values of a given x. It is shown that using ERSSs can reduce the necessary sample size by a factor of 1.33 to 4 when estimating the median of the distribution. Asymptotic results for the estimation of the distribution function is given for the center of the distribution function. Data on the bilirubin level of babies in neonatal intensive care is used to illustrate the method.