A RatioType Estimator for the Estimation of Population Variance using Quartiles of an Auxiliary Variable

Improved ratio-type estimators of finite population variance using quartiles

“…It is observed from Tables 2 and 3 that all the ratio-type estimators T k , (k = 1, 2, ..., 6) which are members of proposed ratio-type estimator T performed better than the usual unbiased estimator s 2 y , usual ratio estimator t 1 due to [1] and the estimators t j , (j = 2, 3, 4, 5) due to [2] for all α ∈ (0.0, 1.0). However all the ratio-type estimators T k , (k = 1, 2, ..., 6) are more efficient than the estimators t j , (j = 6, 7, ..., 12) due to [12,13,14] and [3] for a specific value of α. The estimators T 2 and T 5 which utilize the information on (β 2 (x), Q 2 ) and (ρ, Q d ) respectively are the best in the sense of having largest percent relative efficiency among all the estimators discussed here for α = 1.…”

“…The performance of the ratio-type estimators T k , (k = 1, 2, ..., 6) which are members of the suggested ratio-type estimator T are evaluated against the usual unbiased estimator s 2 y and the estimators t j , (j = 1, 2, ..., 13) which are due to [1], [2], [12,13,14] and [3] respectively. for the population data set [Source: [4]] summarized in Table 1.…”

“…We have known that the value of quartiles and their functions are unaffected by the extreme values or the presence of outliers in the population values. For this reason, [3] and [12,13,14] have considered the problem of estimating the population variance of the study variable using information on variance, quartiles, inter-quartile range, semi-quartile range and semi-quartile average of an auxiliary variable. In this paper our main goal is to estimate the unknown population variance of the study variable by improving the estimators suggested previously using same information on an auxiliary variable such as quartiles, inter-quartile range, semi-quartile range, semi-quartile average etc.…”

“…The suggested estimators have been compared with the usual unbiased and ratio estimators and the estimators due to [2], [12,13,14] and [3]. An empirical study is also carried out to judge the merits of the proposed estimator over other existing estimators of population variance using natural data set.…”

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

“…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.…”