Efficient estimation of cumulative distribution function using moving extreme ranked set sampling with application to re
- PDF / 1,280,139 Bytes
- 18 Pages / 439.37 x 666.142 pts Page_size
- 70 Downloads / 227 Views
Efficient estimation of cumulative distribution function using moving extreme ranked set sampling with application to reliability Ehsan Zamanzade1 · M. Mahdizadeh2 · Hani M. Samawi3 Received: 30 October 2019 / Accepted: 11 May 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this article, we consider the problem of estimating cumulative distribution function (CDF) and a reliability parameter using moving extreme ranked set sampling (MERSS). Two different CDF estimators are described and compared with their competitors in simple random sampling (SRS) and ranked set sampling (RSS). It turns out the CDF estimators in MERSS can be more efficient than their competitors in SRS and RSS at a point in a particular tail of the distribution when the quality of rankings is sufficiently good. Motivated by this efficiency gain, we develop some estimators for the stress-strength probability using MERSS. The suggested estimators are then compared with their counterparts in the literature via Monte Carlo simulation. Finally, a real dataset is used to show the applicability of the developed procedures. Keywords Judgment ranking · Ranked set sampling · Stress-strength probability Mathematics Subject Classification 62D05 · 62F03
* Ehsan Zamanzade [email protected]; [email protected]
M. Mahdizadeh [email protected]; [email protected]
Hani M. Samawi [email protected] 1
Department of Statistics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan 81746‑73441, Iran
2
Department of Statistics, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran
3
Department of Biostatistics, Epidemiology and Environmental Health Sciences, Jiann‑Ping Hsu College of Public Health, Georgia Southern University, Statesboro, GA, USA
13
Vol.:(0123456789)
E. Zamanzade et al.
1 Introduction When exact quantification of sample units is hard or expensive, but assigning a judgment rank to each of them, in a set of small size, is easy and cheap, ranked set sampling (RSS) is a cost-efficient alternative to usual simple random sampling (SRS). It usually leads to improved statistical inference with respect to what is possible in SRS of comparable size. This sampling scheme involves randomly drawing m sets of size m from the population of interest and ranking each set of size m in increasing magnitude of the variable of interest. The ranking is done either visually or using any inexpensive method which does not need the exact quantification of the units. Finally, the sample unit with judgment rank i ( i = 1, … , m ) is selected for actual quantification from the ith set. The entire process is repeated r times (cycle) if required to obtain{a larger sample of size n = rm} , and the resulting ranked set sample is denoted by X[i]j ∶ i = 1, … , m;j = 1, … , r , where X[i]j is the measurement of the ith judgment order statistic from a sample of size m in the jth cycle. Although RSS was proposed by McIntyre (1952) for estimating the average of pasture yield in Austral
Data Loading...
