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

F: The median estimator (exponential product-type) following Bahl and Tuteja (1991) is given by � = � � � − + � � � � � = 2 (4 1 − 1) 8 � � � = 2 � 2 + 2 4 (1 + 4 1 )� (6) G: The median estimator (alternative exponential) due to Enang et.al. (2016) is given by � = 1 � � � − � + � �� + 2 � � � � − + � �� � � � = 2 (4 1 − 8 1 2 + 1) � � � = 2 2 (1 − 2 ) (7) H: Shabbir and Gupta (2017) suggested generalized difference-type estimator for population median as � = � 1 � + 2 � − � �� �� + � + � � 2 � − � � �( − 1) + � � + 2 �� where 1 and 2 are unknown constants whose values are to be determined. Let and are defined to be unknown population parameters and 1 , 2 and are scalar quantities which can take different values like 1 = = 0 and 2 = = = 1 At the optimum values of 1( ) = 1− 1 2 2 1+ 2 �1− 2 � and 2( ) = �1 + 1( ) � − 2�� The expressions for the bias and the mean square error up to the first order of approximation are as follows: � � � ≅ � 1( ) − 1� + 2( ) � � 3 8 2 − � + 2 � and � � � ≅ 2 1+ 2 �1− 2 � � 2 �1 − 2 � �1 − 2 � − 1 4 4 � (8) 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 40 ( F ) Version I N otes