Properties of Exponential Ratio Type Estimators in Equal Probability Sampling: A Simulation Study

Abstract

In this paper, the properties and goodness of fit of exponential ratio type estimator proposed by Khan et al. (Sci Int (Lahore) 26(5):1897–1902, 2014) have been carried out through simulation. It has been shown that estimator is consistent; the convergence of mean and variance of the estimator are discussed. The properties of some existing estimators based on simulation study have also been discussed. Goodness of fit test on the estimator has been carried out using Kolmogorov–Smirnov, Anderson–Darling, Cramer–von Mises and Chi-square statistics. Few standard distributions such as normal, Student t, Weibull and Cauchy distributions are fitted on the estimator. The best-fitted distribution on the estimator turned out to be normal distribution.

Keywords

Goodness of fit / Distribution / Skewed / Consistent / Convergence

References

[1] Bhal S, Tuteja RK. Ratio and product type exponential estimator. J. Inf. Optim. Sci.. 1991, 12 159-163

[2] Cochran WG. Sampling Techniques. 1977 New York: Wiley

[3] Kadilar C, Cingi H. Ratio estimators in stratified random sampling. Biom. J.. 2003, 45 2 218-225

[4] Khan, H.: A class of generalized estimators of population mean using auxiliary variables in single and two phase sampling with properties of the estimators. Unpublished Ph.D. thesis, Department of Statistics, GC University, Lahore, Pakistan (2016)

[5] Khan H, Sanaullah A, Khan MA, Siddiqi AF. Improved exponential ratio type estimators for estimating population mean regarding full information in survey sampling. Sci. Int. (Lahore). 2014, 26 5 1897-1902

[6] Mishra, P., Singh, R.: A new log-product-type estimator using auxiliary information

[7] Oral E, Kadilar C. Robust ratio-type estimators in simple random sampling. J. Korean Stat. Soc.. 2011, 40 4 457-467

[8] Pandey BN, Dubey V. Modified product estimators using coeifficient of variation of auxiliary variate. Assam Stat. Rev.. 1988, 2 64-66

[9] Robson DS. Application of multivariate polykays to the theory of unbiased ratio-type estimation. J. Am. Stat. Assoc.. 1957, 52 511-522

[10] Singh HP, Tailor R. Use of known correlation coefficient in estimating the finite population mean. Stat. Transit.. 2003, 6 555-560

[11] Sisodia BVS, Dwivedi VK. Modified ratio estimator using coefficient of variation of auxiliary variable. J. Indian Soc. Agric. Stat.. 1981, 33 13-18

[12] Srinivas J, Boiroju NK, Reddy MK. Comparison of ratio estimators of population mean. Int. J. Math. Sci. Technol. Humanit.. 2013, 108 1158-1163

[13] Wang, H.-M.: Comparison of the Goodness-of-Fit Tests: the Pearson Chi-square and Kolmogorov-Smirnov Tests. Metrol. Manag. J. 6(1), 57–64 (2009). ISSN 1812-8572