Testing skew-symmetry based on extreme ranked set sampling

Cost-effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time-consuming. In this article, we investigate ratio-type estimators of the population mean of the study variable, involving either the first or the third quartile of the auxiliary variable, using ranked set sampling (RSS) and extreme ranked set sampling (ERSS) schemes. The properties of the estimators are obtained. The estimators in RSS and ERSS are compared to their counterparts in simple random sampling (SRS) for normal data. The numerical results show that the estimators in RSS and ERSS are significantly more efficient than their counterparts in SRS.

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On Regression Estimators Using Extreme Ranked Set Samples

Sultan Qaboos University Journal for Science [SQUJS] ◽

10.24200/squjs.vol9iss0pp67-86 ◽

2004 ◽

Vol 9 ◽

pp. 67

Author(s):

Hani M. Samawi ◽

Ahmed Y.A. Al-Samarraie ◽

Obaid M. Al-Saidy

Keyword(s):

Random Sampling ◽

Sampling Method ◽

Simple Random Sampling ◽

Auxiliary Variable ◽

Ranked Set Sampling ◽

Population Mean ◽

Concomitant Variable ◽

Regression Estimators ◽

Monte Carlo Evaluation ◽

Extreme Ranked Set Sampling

Regression is used to estimate the population mean of the response variable, , in the two cases where the population mean of the concomitant (auxiliary) variable, , is known and where it is unknown. In the latter case, a double sampling method is used to estimate the population mean of the concomitant variable. We invesitagate the performance of the two methods using extreme ranked set sampling (ERSS), as discussed by Samawi et al. (1996). Theoretical and Monte Carlo evaluation results as well as an illustration using actual data are presented. The results show that if the underlying joint distribution of and is symmetric, then using ERSS to obtain regression estimates is more efficient than using ranked set sampling (RSS) or simple random sampling (SRS).

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Reliability Estimation of Inverse Lomax Distribution Using Extreme Ranked Set Sampling

Advances in Mathematical Physics ◽

10.1155/2021/4599872 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Amer Ibrahim Al-Omari ◽

Amal S. Hassan ◽

Naif Alotaibi ◽

Mansour Shrahili ◽

Heba F. Nagy

Keyword(s):

Ranked Set Sampling ◽

Reliability Estimation ◽

Simple Random Sample ◽

Stress Distributions ◽

Reliability Estimate ◽

Lomax Distribution ◽

Set Size ◽

Reliability Estimates ◽

Inverse Lomax Distribution ◽

Extreme Ranked Set Sampling

In survival analysis, the two-parameter inverse Lomax distribution is an important lifetime distribution. In this study, the estimation of R = P Y < X is investigated when the stress and strength random variables are independent inverse Lomax distribution. Using the maximum likelihood approach, we obtain the R estimator via simple random sample (SRS), ranked set sampling (RSS), and extreme ranked set sampling (ERSS) methods. Four different estimators are developed under the ERSS framework. Two estimators are obtained when both strength and stress populations have the same set size. The two other estimators are obtained when both strength and stress distributions have dissimilar set sizes. Through a simulation experiment, the suggested estimates are compared to the corresponding under SRS. Also, the reliability estimates via ERSS method are compared to those under RSS scheme. It is found that the reliability estimate based on RSS and ERSS schemes is more efficient than the equivalent using SRS based on the same number of measured units. The reliability estimates based on RSS scheme are more appropriate than the others in most situations. For small even set size, the reliability estimate via ERSS scheme is more efficient than those under RSS and SRS. However, in a few cases, reliability estimates via ERSS method are more accurate than using RSS and SRS schemes.

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