Jñānābha‎, Vol. 48 (1) (2018), 26-52

ESTIMATION OF POPULATION MEAN USING RATIO TYPE ESTIMATORS UNDER SIMPLE RANDOM SAMPLING SCHEME: A REVIEW

by

S. K. Yadav
Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, Uttar Pradesh, India
Sheela Misra
Department of Statistics, University of Lucknow, Lucknow-226007, Uttar Pradesh, India
H. N. Dhungana
Department of Community Medicine, Integral Institute of Medical Sciences and Research,Lucknow, Uttar Pradesh, India
S. S. Mishra
Department of Mathematics and Statistics (A Centre of Excellence) Dr RML Avadh University, Faizabad-224001, Uttar Pradesh, India


Abstract

 The present manuscript is a critical and chronological review of the ratio type estimators of population mean of the study variable using auxiliary information on a single auxiliary variable. In this paper various ratio type estimators of population mean in the literature have been given chronologically. The large sample properties that is biases and the mean squared errors of these ratio type estimators of population mean have been given up to the first order of approximation. The expressions of the bias and the mean squared error of every mentioned estimator have been given. The optimum values of the characterizing scalars have been given for the generalized type estimators having characterizing scalars and the minimum values of the mean squared errors of corresponding estimators have been obtained for these optimum values of the characterizing scalars. This work is believed to provide insightful gain in systematic manner for the researchers who are engaged in the field to explore it through serious investigation. 

2010 Mathematics Subject Classification. 62D05 
Keywords and phrases. Auxiliary variable, Parameter, Estimator, Bias, Mean Squared Error, Efficiency.