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L-Moments Based Calibrated Variance Estimators Using Double Stratified Sampling

Usman Shahzad1,2,*, Ishfaq Ahmad1, Ibrahim Mufrah Almanjahie3,4, Nadia H.Al –Noor5

1 Department of Mathematics and Statistics, International Islamic University, Islamabad, 44000, Pakistan
2 Department of Mathematics and Statistics, PMAS-Arid Agriculture University, Rawalpindi, 46300, Pakistan
3 Department of Mathematics, College of Science, King Khalid University, Abha, 62529, Saudi Arabia
4 Statistical Research and Studies Support Unit, King Khalid University, Abha, 62529, Saudi Arabia
5 Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, 10011, Iraq

* Corresponding Author: Usman Shahzad. Email:

Computers, Materials & Continua 2021, 68(3), 3411-3430.


Variance is one of the most vital measures of dispersion widely employed in practical aspects. A commonly used approach for variance estimation is the traditional method of moments that is strongly influenced by the presence of extreme values, and thus its results cannot be relied on. Finding momentum from Koyuncu’s recent work, the present paper focuses first on proposing two classes of variance estimators based on linear moments (L-moments), and then employing them with auxiliary data under double stratified sampling to introduce a new class of calibration variance estimators using important properties of L-moments (L-location, L-cv, L-variance). Three populations are taken into account to assess the efficiency of the new estimators. The first and second populations are concerned with artificial data, and the third populations is concerned with real data. The percentage relative efficiency of the proposed estimators over existing ones is evaluated. In the presence of extreme values, our findings depict the superiority and high efficiency of the proposed classes over traditional classes. Hence, when auxiliary data is available along with extreme values, the proposed classes of estimators may be implemented in an extensive variety of sampling surveys.


Cite This Article

U. Shahzad, I. Ahmad, I. Mufrah Almanjahie and N. H.Al –Noor, "L-moments based calibrated variance estimators using double stratified sampling," Computers, Materials & Continua, vol. 68, no.3, pp. 3411–3430, 2021.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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