Global Journal of Science Frontier Research, F: Mathematics and Decision Science, Volume 21 Issue 4

And the optimum bias becomes � � ( )� = � 3 8 2 − 2 2 + � (15) a) A Case of Two Variables under Simple Random Sampling � ∗ ( ) = � � � + (1 − ) � � � ( � − ) ( + � ) � (16) � � ∗ ( )� = � 2 + 3 8 2 + (1 − 2 ) − (1 − 2 ) 2 − 2 � (17) � � ∗ ( )� = 2 � 2 + (1 − 2 ) 2 2 + 2 4 − (1 − 2 ) + 2(1 − 2 ) − � (18) Minimizing (18) with respect to gives = 2 2 +2 − 4 2 Substituting into (18) gives � � ∗ ( )� = 2 � 2 �1 − 2 � + 2 4 �1 − 2 � + � − �� � � ∗ ( )� = 2 � 2 + 2 4 − � 2 2 − 1 � 2 − � (19) And the minimum bias given as � � ∗ ( )� = � 2 2 + 3 8 2 + 2 − 4 − 2 2 − 2 2 4 − 2 + � (20) b) Application The bias and MSE values of the existing and proposed estimators are computed using two different populations under simple random sampling. The percent relative efficiencies of the estimators are obtained as follows: % = ( � ) (. ) × 100 where ( � ) is the MSE of classical median estimator while (. ) denotes the MSE of estimators mentioned here. The population statistics and the results of analyses are shown as follows: Towards the Efficiency of the Ratio Estimator for Population Median in Survey Sampling © 2021 Global Journals 1 Global Journal of Science Frontier Research Volume XXI Issue IV Year 2021 42 ( F ) Version I N otes