Title: Refined descriptive sample inference in the estimation of the cumulative distribution function

Authors: Oualid Saci; Megdouda Ourbih-Tari

Addresses: Laboratory of Applied Mathematics, Faculty of Exact Sciences, University of Bejaia, 06000, Bejaia, Algeria ' Institut des Sciences, Centre Universitaire Morsli Abdellah de Tipaza, 42020, Tipaza, Algeria; Laboratory of Applied Mathematics, Faculty of Exact Sciences, University of Bejaia, 06000, Bejaia, Algeria

Abstract: In this paper, we compare the estimators of the cumulative distribution function obtained by the refined descriptive (RD) sample and simple random (SR) sample, and show that the one obtained by RD sample is more efficient than that obtained by SR sample. For this purpose, we have compared the probability structure of RD sample and SR sample where the latter is generated using the principle of the RD sampling method. Simulation results of different distributions are given to validate the proposed theoretical comparison.

Keywords: refined descriptive sampling; RDS; Monte Carlo method; statistic order; multinomial vector; cumulative distribution function; cdf.

DOI: 10.1504/IJMOR.2021.112938

International Journal of Mathematics in Operational Research, 2021 Vol.18 No.2, pp.264 - 287

Received: 31 Dec 2018
Accepted: 31 Dec 2019
Published online: 10 Feb 2021 *

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