Improving Efficiencies of Ratio- and Product-type Estimators for Estimating Population Mean for Time-based Survey

  • Priyanka Chhaparwal Department of mathematics, University of Engineering and Management, Gurukul, Sikar Road, Near Udaipuria Mod, Jaipur, Rajasthan 303807, India
  • Sanjay Kumar Department of Statistics, Central University of Rajasthan, Bandarsindri, Kishangarh-305817, Ajmer, Rajasthan, India
Keywords: Ratio estimator, product estimator, auxiliary variable, coefficient of variation, HEWMA, simulation study

Abstract

Statisticians often use auxiliary information at an estimation stage to increase efficiencies of estimators. In this article, we suggest modified ratio- and product-type estimators utilizing the known value of the coefficient of variation of the auxiliary variable for a time-based survey. Further, to excel the performance of the suggested estimators, we utilize information from the past surveys along with the current surveys through hybrid exponentially weighted average. We obtain expressions for biases and mean square errors of the suggested estimators. The conditions, under which the suggested estimators have less mean square errors than that of other existing estimators, are also obtained. The results obtained through an empirical analysis examine the use of information from past surveys along with current surveys and show that the mean square errors and biases of the suggested estimators are less than that of the existing estimators. For example: for a sample size 5, mean square error and bias of the suggested ratio-type estimator are (0.0414,0.0065) which are less than (0.5581,0.0944) of the existing Cochran (1940) estimator, (0.4788,0.0758), of Sisodia and Dwivedi (1981) estimator and (0.0482,0.0082) of Muhammad Noor-ul-Amin (2020) estimator. Similarly, mean square error and bias of the suggested product- type estimator are (0.0025,−0.0006) which are less than (0.0612,−0.0096) of the existing Murthy (1964) estimator, (0.0286,−0.0071), of Pandey and Dubey (1988) estimator and (0.0053,−0.0008) of Muhammad Noor-ul-Amin (2020) estimator.

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Author Biographies

Priyanka Chhaparwal, Department of mathematics, University of Engineering and Management, Gurukul, Sikar Road, Near Udaipuria Mod, Jaipur, Rajasthan 303807, India

Priyanka Chhaparwal received her Ph.D. from Central University of Rajasthan, Ajmer, Rajasthan. She is currently working as an Assistant professor at the Department of mathematics, University of Engineering and Management, Gurukul, Jaipur, Rajasthan, India. Her research area includes estimating problems in sampling theory.

Sanjay Kumar, Department of Statistics, Central University of Rajasthan, Bandarsindri, Kishangarh-305817, Ajmer, Rajasthan, India

Sanjay Kumar obtained his Ph.D from Banaras Hindu University, Varanasi, India. He has been working as an Assistant Professor since metricconverterProductID2011 in2011 in the Department of Statistics, Central University of Rajasthan, Ajmer, Rajasthan, India. His research interests include estimation, optimization problems and robustness study in sampling theory.

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Published
2022-05-07
Section
Articles