Estimation for the Parameters of Power Rayleigh Distributions Using Double Ranked Set Sampling with an Application to Wind Speed Data

Abstract

In this paper, we propose to use Power Rayleigh (PR) distribution for parameter estimation under simple random sampling (SRS), ranked set sampling (RSS) and double ranked set sampling (DRSS) schemes. The sampling technique plays an important role in statistical parameter estimation problems. In the current paper, DRSS, RSS, and SRS are considered for the estimation of parameters concerning PR distribution. The maximum likelihood (ML) and the method of moment (MoM) estimators are considered and their properties are studied. An extensive Monte Carlo simulation study is conducted to assess the performances of the ML and MOM estimators in terms of biases and mean square errors (MSEs) based on DRSS, RSS, and SRS schemes. In the application part of the study, PR distribution is used for modeling the wind speed data collected on a seasonal maximum daily basis from the Giresun site, Turkey in 2016 to illustrate the usefulness of RSS and DRSS schemes under different estimators. The results show that the MOM estimator under DRSS is significantly more efficient than the SRS and RSS schemes.