Estimation of Distribution Function using Percentile Ranked Set Sampling

Abstract

The estimation of distribution function has received considerable attention in the literature. Because, many practical problems involve estimation of distribution function from experimental data. Estimating the distribution function makes it possible to do pointwise estimation and to make statistical inference about the distribution of interested population. In this study, we suggested an empirical distribution function (EDF) for percentile ranked set sampling (PRSS). Bias of the EDF estimator is investigated theoretically and numerically. Relative efficiencies of the proposed EDF estimator based on PRSS with respect to EDF estimator based on simple random sampling (SRS) and ranked set sampling (RSS) are obtained. We also considered impact of imperfect rankings on the EDF based on PRSS. According to the results, the proposed EDF estimator is unbiased for the extreme ”minimum and maximum” points and center of the distribution. Also, it is clearly appeared that the EDF estima[1]tor based on PRSS is more efficient than the EDF based on SRS. Another important result is that the suggested EDF estimator has larger efficiencies than the EDF based on RSS for some special cases of PRSS. In the application, the EDF based on PRSS is used to estimate the proportion of women in obesity class III (BMI> 40).