Ranked Set Sampling Measure of the Overlapping Coefficients for Two Rayleigh Distribution

In this paper we deal with overlap(OVL) coefficients of two Rayleigh distributions, using ranked set sampling(RSS). As overlap coefficients, Matusita’s measure ρ, Morisita’s measure λ, Weitzman’s measure Δ are well known, and they measure the similarity, the agreement or the closeness of the two probability distributions. We define the overlap coefficients in Rayleigh distributions and compare asymptotic relative efficiencies(ARE) of them, using RSS relative to simple random sampling(SRS). As results of comparison, to use the RSS for estimation of three overlap coefficients is more efficient than to use the SRS. We estimate the OVL coefficients by Taylor series expansion and delta method. Later we wish to improve OVL coefficients under several sampling techniques and several distributions.