Abstract:Partial ranked set sampling (PRSS) is a cost-effective sampling method. It is a combination of simple random sample (SRS) and ranked set sampling (RSS) designs. The PRSS method allows flexibility for the experimenter in selecting the sample when it is either difficult to rank the units within each set with full confidence or when experimental units are not available. In this article, we introduce and define the likelihood function of any probability distribution under the PRSS scheme. The performance of the ma… Show more
“…The ML estimators of , and are derived by solving numerically Equation (8), Equation (9) and Equation (10) using an iterative method, As a Result, , uv is obtained using Equation (4).…”
Section: Mssr Estimator Using Nrssmentioning
confidence: 99%
“…i. Take (n, m) = (2, 2), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8), (9,9), where n and m are set sizes. ii.…”
Section: Simulation Studymentioning
confidence: 99%
“…The superiority of RSS and its variations in estimating a wide range of population metrics has been demonstrated in several investigations. Reference [9] used an extreme RSS approach to test for exponentiated Pareto distribution. Reference [10] used RSS to develop parameter estimators for the Zubair Lomax distribution.…”
In this study, we analyze a multicomponent system with v independent and identical strength components X1, …, Xv and each of these components is exposed to a common random stress Y. The system is considered to be operating only if at least u out of v (1 u v) strength variables exceeds the random stress. The estimate of system reliability is investigated, assuming strength and stress random variables follow the exponentiated exponential distribution with different shape parameters. The maximum likelihood estimator for system reliability is derived from ranked set sampling (RSS), neoteric RSS (NRSS) and median RSS (MRSS). Some accuracy measurements, such as mean squared errors and efficiencies, are used to examine the behaviour of various estimators. Simulation studies demonstrate that the NRSS scheme's reliability estimates are chosen above those of the RSS and MRSS schemes in the majority of situations. Theoretical research is explained through real data analysis
“…The ML estimators of , and are derived by solving numerically Equation (8), Equation (9) and Equation (10) using an iterative method, As a Result, , uv is obtained using Equation (4).…”
Section: Mssr Estimator Using Nrssmentioning
confidence: 99%
“…i. Take (n, m) = (2, 2), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8), (9,9), where n and m are set sizes. ii.…”
Section: Simulation Studymentioning
confidence: 99%
“…The superiority of RSS and its variations in estimating a wide range of population metrics has been demonstrated in several investigations. Reference [9] used an extreme RSS approach to test for exponentiated Pareto distribution. Reference [10] used RSS to develop parameter estimators for the Zubair Lomax distribution.…”
In this study, we analyze a multicomponent system with v independent and identical strength components X1, …, Xv and each of these components is exposed to a common random stress Y. The system is considered to be operating only if at least u out of v (1 u v) strength variables exceeds the random stress. The estimate of system reliability is investigated, assuming strength and stress random variables follow the exponentiated exponential distribution with different shape parameters. The maximum likelihood estimator for system reliability is derived from ranked set sampling (RSS), neoteric RSS (NRSS) and median RSS (MRSS). Some accuracy measurements, such as mean squared errors and efficiencies, are used to examine the behaviour of various estimators. Simulation studies demonstrate that the NRSS scheme's reliability estimates are chosen above those of the RSS and MRSS schemes in the majority of situations. Theoretical research is explained through real data analysis
“…The summarize of the literature about parameter estimation based on the RSS schemes. Author RSS Scheme Distribution Helu et al [41] RSS Weibull Al-Omari and Al-Hadhrami [42] ERSS Modified Weibull Elbatal [43] RSS Log-logistic Omar and Ibrahim [44] RSS, MRSS, ERSS Pareto Hassan [45] RSS Exponentiated exponential Hussian [46] RSS Kumaraswamy Yousef and Al-Subh [47] RSS Gumbel Koshti and Kamalja [48] RSS Bivariate Lomax Khamnei and Abusalah [49] RSS Generalized logistic Dey et al [50] RSS, MRSS Rayleigh Esemen and Gürler [51] RSS, MRSS, ERSS Generalized Rayleigh He et al [52] RSS Log-logistic Samuh et al [53] RSS, MRSS, ERSS Weibull-Pareto Taconeli and Giolo [54] RSS Power Lindley, weighted Lindley…”
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.
“…The MLEs of the parameters for the inverted Topp-Leone and generalized exponential distributions, were considered, respectively, by Refs. [17,18]. For more research on RSS-based reliability estimate [19,20,21,22,23].…”
Effective sample design has a major role in the quality of parameter estimation in statisticalparameter estimation issues. The ranking set sampling (RSS) strategy is effective and a less costlyoption than simple random sampling (SRS). A novel mixture continuous lifetime distribution thathas been proposed recently is the power Chris-Jerry distribution (PC-JD). It is useful for modelinga number of real data sets. This paper investigates the RSS approach for estimating the PC-JD’sparameters. There are roughly sixteen different techniques of estimation that are used, such as themaximum likelihood method, the percentiles method, some methods based on minimum distance,the Kolmogorov method, and some methods based on minimum and maximum spacing distances. Incomparison to a SRS, the simulation research assesses the performance of the suggested RSS-basedestimates in terms of some measures of accuracy. To identify the optimal estimating strategy, thepartial and overall ranks of many estimates are shown. According to numerical results, the maximumlikelihood approach seems to be quite beneficial in evaluating the estimated quality of RSS and SRS.RSS is a more effective sampling approach than SRS owing to its better efficiency. Additionally, thedifferent estimation techniques with survival data for both sampling techniques are examined
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