Improved ratio-type estimators of finite population variance using quartiles

Singh, Housila P.; Pal, Surya K.; Solanki, Ramkrishna S.

doi:10.15672/hjms.2014448247

Cited by 9 publications

(20 citation statements)

References 15 publications

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“…The Estimation of population variance along with the estimation of population mean is of interest in many practical situations such as business, manufacturing industry, Services industry, the pharmaceutical industry, medical sciences, biological sciences and agriculture (cf. Solanki et al, [1]). Therefore, the development of efficient estimators of population variance constantly attracts the researchers.…”

Section: Introductionmentioning

confidence: 99%

“…Generally, the information of conventional auxiliary parameters such as the coefficient of kurtosis, the coefficient of skewness, the coefficient of variation, and the coefficient of correlation is used in a linear combination with the sample information of the study and the auxiliary variable to design the estimators of population variance. For instance, see Isaki [9]; Upadhyaya and Singh [10]; Kadilar and Cingi [11]; Subramani and Kumarapandiyan [12][13][14]; Khan and Shabbir [15]; Solanki et al, [1]; Yaqub and Shabbir [16]; Maqbool and Javaid [17]; Adichwal, Sharma and Singh [18]; Maji, Singh and Bandyopadhyay [19]; Abid et al, [20]; Singh, Pal and Yadav [21]; Muneer et al, [22] and the references cited therein. The development of ratio-type estimator that deals with the presence of outliers in the data is a neglected area in survey sampling.…”

Section: Introductionmentioning

confidence: 99%

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Enhancing the efficiency of the ratio-type estimators of population variance with a blend of information on robust location measures

et al. 2019

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Numerous ratio-type estimators of the population variance are proposed in the existing literature based on different characteristics of the study as well as the auxiliary variable. However, mostly the existing estimators are based on the conventional measures of the population characteristics and their efficiency is dubious in the presence of outliers in the data. This study presents improved families of variance estimators under simple random sampling without replacement assuming that the information on some robust nonconventional location parameters of the auxiliary variable is known besides the usual conventional parameters. The bias and mean square error of the proposed families of estimators are obtained and the efficiency conditions are derived mathematically. The theoretical results are supplemented with the numerical illustrations by using real datasets which indicates the supremacy of the suggested families of estimators.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Enhancing the efficiency of the ratio-type estimators of population variance with a blend of information on robust location measures

et al. 2019

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“…Mostly coefficient of skewness, coefficient of kurtosis, coefficient of variation, and coefficient of correlation are used in linear combination with some other conventional parameters of the auxiliary variable to estimate the variance. The readers can refer to [4][5][6][7][8][9][10][11][12][13][14][15] and the references therein. The auxiliary measures used in most of the existing ratio-type estimators of variance are nonresistant to the presence of outliers or nonsymmetrical populations.…”

Section: Introductionmentioning

confidence: 99%

Use of Nonconventional Dispersion Measures to Improve the Efficiency of Ratio-Type Estimators of Variance in the Presence of Outliers

et al. 2019

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The use of auxiliary information in survey sampling to enhance the efficiency of the estimators of population parameters is a common phenomenon. Generally, the ratio and regression estimators are developed by using the known information on conventional parameters of the auxiliary variables, such as variance, coefficient of variation, coefficient of skewness, coefficient of kurtosis, or correlation between the study and auxiliary variable. The efficiency of these estimators is dubious in the presence of outliers in the data and a nonsymmetrical population. This study presents improved variance estimators under simple random sampling without replacement with the assumption that the information on some nonconventional dispersion measures of the auxiliary variable is readily available. These auxiliary variables can be the inter-decile range, sample inter-quartile range, probability-weighted moment estimator, Gini mean difference estimator, Downton's estimator, median absolute deviation from the median, and so forth. The algebraic expressions for the bias and mean square error of the proposed estimators are obtained and the efficiency conditions are derived to compare with the existing estimators. The percentage relative efficiencies are used to numerically compare the results of the proposed estimators with the existing estimators by using real datasets, indicating the supremacy of the suggested estimators.

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“…Keeping this fact in view, a large number of authors have paid their attention toward the formulation of modified ratio and product estimators using information on an auxiliary variate, for instance, see [10] and Singh et al [11].…”

Section: Introductionmentioning

confidence: 99%

Approximation of Finite Population Totals Using Lagrange Polynomial

Kabareh¹,

Mageto²,

Muema³

2017

OJS

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Approximation of finite population totals in the presence of auxiliary information is considered. A polynomial based on Lagrange polynomial is proposed. Like the local polynomial regression, Horvitz Thompson and ratio estimators, this approximation technique is based on annual population total in order to fit in the best approximating polynomial within a given period of time (years) in this study. This proposed technique has shown to be unbiased under a linear polynomial. The use of real data indicated that the polynomial is efficient and can approximate properly even when the data is unevenly spaced.

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Improved ratio-type estimators of finite population variance using quartiles

Cited by 9 publications

References 15 publications

Enhancing the efficiency of the ratio-type estimators of population variance with a blend of information on robust location measures

Enhancing the efficiency of the ratio-type estimators of population variance with a blend of information on robust location measures

Use of Nonconventional Dispersion Measures to Improve the Efficiency of Ratio-Type Estimators of Variance in the Presence of Outliers

Approximation of Finite Population Totals Using Lagrange Polynomial

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