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

Population 1: 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 ; = 17 ; = 2068 ; = 2011 ; = 2307 ; = 0.1505 ; = 0.1431 ; = 0.3166 ; ( ) = 0.00014 ; ( ) = 0.00014 ; and ( ) = 0.00013 . Population 2: Let as the U.S. exports to Singapore in billions of Singapore dollars, as the money supply figures in billions of Singapore dollars and is the local supply in U.S. dollars given by Aczel and Sounderpandian (2004). = 67 ; = 23 ; = 4.8 ; = 7.0 ; = 151 ; = 0.6624 ; = 0.7592 ; = 0.8624 ; ( ) = 0.0763 ; ( ) = 0.0526 ; and ( ) = 0.0024 ; Table 1: Results for Simple Random Sampling Population I Population II Estimator Absolute bias MSE PRE Absolute bias MSE PRE � 0 565443.6 100 0 1.23 100 � 246.3 988372.8 57.2 0.08 0.82 150 � 87.27 627420.2 90.1 0.01 0.72 170.8 � 373.78 3307296 17.1 0.59 9.31 13.2 � 42.32 1338418 42.2 0.17 4.06 30.3 � 14.98 802442.8 70.5 0.05 2.34 52.6 � 408.87 552636.1 102.3 0.03 0.69 178.3 � 3373.88 491568.8 115.0 1.54 0.52 236.5 � 46089.73 502378.1 112.6 0.48 0.31 396.8 � ( ) 144.55 552636.1 102.3 0.15 0.69 178.3 � ∗ ( ) 207.98 520612.8 108.6 0.13 0.38 323.7 c) Median Estimators under Two Phase Sampling Consider a finite population with Nunits = { 1 , 2 , … , } . The ℎ unit ofthe population values forthe study variable , auxiliary variables and are ; and respectively. Under two-phase sampling design, a sample of size ′ is drawn using simple random sampling without replacement at first phase and the values on and are obtained on the units of the sample. In second phase, a simple random samplingwithout replacement criteria is used for drawing sample of size from the first phasesample and the values on the variables ; and are taken on selected units.To obtain the properties of the proposed median estimator under two-phase samplingscheme the following existing estimators are summarized as; i) Singh, Joarder, and Tracy suggested a ratio estimator for median in two phase Sampling � = � � � ′ � � � = � 1 − 1 ′ � �1 − � 4 ( Towards the Efficiency of the Ratio Estimator for Population Median in Survey Sampling 1 Global Journal of Science Frontier Research Volume XXI Issue IV Year 2021 43 ( F ) © 2021 Global Journals Version I N otes