On optimal classes of estimators under ranked set sampling

Bhushan, Shashi; Kumar, Anoop

doi:10.1080/03610926.2020.1777431

Cited by 28 publications

(18 citation statements)

References 21 publications

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“…From the perusal of the numerical results reported in Tables 1–9, we have the following observations. The results of the empirical study presented in Table 1 for real populations show the superiority of the proposed estimators

{T}_{a{k}_1}

over the usual mean estimator

{T}_m

, usual ratio estimator

{T}_r

, usual regression estimator

{T}_{lr}

, ratio type estimators

{T}_a

and

{T}_w

due to Abu‐Dayyeh et al, 24 Mehta and Mandowara 25 estimator

{T}_{mm}

, Khan and Shabbir 26,27 estimators

{\overline{y}}_{k_i},\kern0.3em i=1,2

, Khan et al 28 estimator

{T}_{k_3}

and Bhushan and Kumar 32 type estimators

{T}_{b{k}_i},\kern0.3em i=1,2,3

…”

Section: Numerical Resultsmentioning

confidence: 99%

“…(ix) Bhushan and Kumar 32 estimators Following Bhushan and Kumar, 32 we define some optimal classes of estimators with bivariate auxiliary information as…”

Section: (V) Mehta and Mandowara 25 Estimatormentioning

confidence: 99%

“…Following Bhushan and Kumar, 32 we define some optimal classes of estimators with bivariate auxiliary information as

{T}_{bk_1}\kern0.5em ={\phi}_1{\overline{y}}_{\left[n\right]}+{\zeta}_1\left({\overline{z}}_{1(n)}-{\overline{Z}}_1\right)+{\zeta}_2\left({\overline{z}}_{2\left[n\right]}-{\overline{Z}}_2\right),

{T}_{bk_2}\kern0.5em ={\phi}_2{\overline{y}}_{\left[n\right]}{\left(\frac{{\overline{Z}}_1}{{\overline{z}}_{1(n)}}\right)}^{\delta_1}{\left(\frac{{\overline{Z}}_2}{{\overline{z}}_{2\left[n\right]}}\right)}^{\delta_2},

…”

Section: Conventional Estimatorsmentioning

confidence: 99%

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New efficient logarithmic estimators using multi‐auxiliary information under ranked set sampling

Bhushan

Kumar

2022

Concurrency and Computation

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Summary This article proposes a new efficient logarithmic class of estimators for estimating the population mean in the case of multi‐auxiliary information using ranked set sampling. The bias and mean square error of the proposed estimators are reported up to the first order of approximation. It is demonstrated analytically and numerically that the proposed estimators are always better than their competitors. We accomplished an empirical study using some real populations and a simulation study using some artificially generated populations to support the analytical comparisons between the proposed estimators and their competitors.

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{T}_{a{k}_1}

over the usual mean estimator

{T}_m

, usual ratio estimator

{T}_r

, usual regression estimator

{T}_{lr}

, ratio type estimators

{T}_a

and

{T}_w

due to Abu‐Dayyeh et al, 24 Mehta and Mandowara 25 estimator

{T}_{mm}

, Khan and Shabbir 26,27 estimators

{\overline{y}}_{k_i},\kern0.3em i=1,2

, Khan et al 28 estimator

{T}_{k_3}

and Bhushan and Kumar 32 type estimators

{T}_{b{k}_i},\kern0.3em i=1,2,3

…”

Section: Numerical Resultsmentioning

confidence: 99%

“…(ix) Bhushan and Kumar 32 estimators Following Bhushan and Kumar, 32 we define some optimal classes of estimators with bivariate auxiliary information as…”

Section: (V) Mehta and Mandowara 25 Estimatormentioning

confidence: 99%

“…Following Bhushan and Kumar, 32 we define some optimal classes of estimators with bivariate auxiliary information as

{T}_{bk_1}\kern0.5em ={\phi}_1{\overline{y}}_{\left[n\right]}+{\zeta}_1\left({\overline{z}}_{1(n)}-{\overline{Z}}_1\right)+{\zeta}_2\left({\overline{z}}_{2\left[n\right]}-{\overline{Z}}_2\right),

{T}_{bk_2}\kern0.5em ={\phi}_2{\overline{y}}_{\left[n\right]}{\left(\frac{{\overline{Z}}_1}{{\overline{z}}_{1(n)}}\right)}^{\delta_1}{\left(\frac{{\overline{Z}}_2}{{\overline{z}}_{2\left[n\right]}}\right)}^{\delta_2},

…”

Section: Conventional Estimatorsmentioning

confidence: 99%

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New efficient logarithmic estimators using multi‐auxiliary information under ranked set sampling

Bhushan

Kumar

2022

Concurrency and Computation

Self Cite

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“…Samawi and Muttlak [12] shown that ranking of the denominator variable of the ratio estimator improves the efficiency. The interested readers may refer to some recent works such as Bhushan and Kumar [13][14][15][16] and Bhushan et al [17,18] for a comprehensive study about RSS. In extensive surveys, when the information on more than one auxiliary variable is available, then, Abu-Dayyeh et al [19] introduced two estimators under RSS for estimating the population mean.…”

Section: Introductionmentioning

confidence: 99%

On Efficient Estimation of the Population Mean under Stratified Ranked Set Sampling

Bhushan

Kumar

Shahab

et al. 2022

Journal of Mathematics

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This paper considers some efficient combined and separate classes of estimators of the population mean in the presence of bivariate auxiliary information under stratified ranked set sampling. The mean square error MSE expressions of the proffered combined and separate classes of estimators are derived to the first order of approximation. The theoretical conditions are obtained under which the proffered combined and separate classes of estimators perform better than the existing combined and separate class of estimators. Subsequently, numerical and simulation studies are performed using real and artificially generated populations. The numerical and simulation results are found to be rewarding, showing the superiority of the proffered estimators over the existing estimators.

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“…[6] considered the modified ratio estimator for the population mean using double MRSS. For more details of RSS and its applications, see [7][8][9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Three-fold utilization of supplementary information for mean estimation under median ranked set sampling scheme

Shahzad

Ahmad²,

Almanjahie³

et al. 2022

PLoS ONE

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Ranked set sampling (RSS) has created a broad interest among researchers and it is still a unique research topic. It has at long last begun to find its way into practical applications beyond its initial horticultural based birth in the fundamental paper by McIntyre in the nineteenth century. One of the extensions of RSS is median ranked set sampling (MRSS). MRSS is a sampling procedure normally utilized when measuring the variable of interest is troublesome or expensive, whereas it might be easy to rank the units using an inexpensive sorting criterion. Several researchers introduced ratio, regression, exponential, and difference type estimators for mean estimation under the MRSS design. In this paper, we propose three new mean estimators under the MRSS scheme. Our idea is based on three-fold utilization of supplementary information. Specifically, we utilize the ranks and second raw moments of the supplementary information and the original values of the supplementary variable. The appropriateness of the proposed group of estimators is demonstrated in light of both real and artificial data sets based on the Monte-Carlo simulation. Additionally, the performance comparison is also conducted regarding the reviewed families of estimators. The results are empowered and the predominant execution of the proposed group of estimators is seen throughout the paper.

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On optimal classes of estimators under ranked set sampling

Cited by 28 publications

References 21 publications

New efficient logarithmic estimators using multi‐auxiliary information under ranked set sampling

New efficient logarithmic estimators using multi‐auxiliary information under ranked set sampling

On Efficient Estimation of the Population Mean under Stratified Ranked Set Sampling

Three-fold utilization of supplementary information for mean estimation under median ranked set sampling scheme

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