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

� � � = 2 2 4 �� 1 ′ − 1 � + � 1 − 1 ′ � 2 − � 1 − 1 � 2 � (24) d) Proposed Median Estimator Under Two Phase Sampling � ( ) = � � � ′ � + (1 − ) � � ′ � � � − � ′ � � + � ′ � � (25) � ( ) = (1 + 0 )[ (1 + 1 ′ )(1 + 1 ) −1 + (1 − )(1 + 1 )(1 + 1 ′ ) −1 ] � − 2 ′ 2 �1 − 2 ′ 2 + 2 ′2 4 �� � � ( )� = � ( − 1 ) 2 + 3 8 1 2 + ( − 1 )(1 − 2 ) − 1 2 � (26) � � ( )� = 2 �( − 1 )(4 2 − 4 + 1) 2 + 1 2 4 + 2 + 2( − 1 )(1 − 2 ) − 1 � (27) For optimum value of the MSE of � ( ) , the value of is given as = 1 +1 2 , then (27) becomes � � ( )� = 2 � 2 − ( − 1 ) 2 2 + 1 2 4 − 1 � (28) And the optimum bias becomes � � ( )� = �( − 1 ) 2 2 + ( − 1 ) 2 + 3 8 1 2 − ( − 1 ) 2 2 − 1 2 � (29) e) Numerical study under two-phase sampling Here three different populations will be considered to validate the theoretical claims of both the existing and the proposed estimators. The population statistics and the results of analyses are shown as follows: Population 3: Let Population 1: Let ; and respectively be the number of fish caught by the marine recreational fisherman in years 1995, 1994 and 1993 in USA given by Singh (2003a). = 69 ; ′ = 24 = 17 ; = 2068 ; = 2011 ; = 2307 ; = 0.1505 ; = 0.1431 ; = 0.3166 ; ( ) = 0.00014 ; ( ) = 0.00014 ; and ( ) = 0.00013 . 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 46 ( F ) Version I N otes