International Scholarly Research Notices

Research Article

Some Improved Multivariate-Ratio-Type Estimators Using Geometric and Harmonic Means in Stratified Random Sampling

Table 1

Data statistics.
𝑁 1 = 1 2 7 𝑁 2 = 1 1 7 𝑁 3 = 1 0 3
𝑁 4 = 1 7 0 𝑁 5 = 2 0 5 𝑁 6 = 2 0 1
𝑛 1 = 3 1 𝑛 2 = 2 1 𝑛 3 = 2 9
𝑛 4 = 3 8 𝑛 5 = 2 2 𝑛 6 = 3 9
𝑆 𝑦 1 = 8 8 3 . 8 3 5 𝑆 𝑦 2 = 6 4 4 . 9 2 2 𝑆 𝑦 3 = 1 0 3 3 . 4 6 7
𝑆 𝑦 4 = 8 1 0 . 5 8 5 𝑆 𝑦 5 = 4 0 3 . 6 5 4 𝑆 𝑦 6 = 7 1 1 . 7 2 3
𝑌 1 = 7 0 3 . 7 4 𝑌 2 = 4 1 3 𝑌 3 = 5 7 3 . 1 7
𝑌 4 = 4 2 4 . 6 6 𝑌 5 = 2 6 7 . 0 3 𝑌 6 = 3 9 3 . 8 4
𝑆 𝑥 1 = 3 0 4 8 6 . 7 5 1 𝑆 𝑥 2 = 1 5 1 8 0 . 7 6 9 𝑆 𝑥 3 = 2 7 5 4 9 . 6 9 7
𝑆 𝑥 4 = 1 8 2 1 8 . 9 3 1 𝑆 𝑥 5 = 8 4 9 7 . 7 7 6 𝑆 𝑥 6 = 2 3 0 9 4 . 1 4 1
𝑋 1 = 2 0 8 0 4 . 5 9 𝑋 2 = 9 2 1 1 . 7 9 𝑋 3 = 1 4 3 0 9 . 3 0
𝑋 4 = 9 4 7 8 . 8 5 𝑋 5 = 5 5 6 9 . 9 5 𝑋 6 = 1 2 9 9 7 . 5 9
𝑆 𝑥 𝑦 1 = 2 5 2 3 7 1 5 3 . 5 2 𝑆 𝑥 𝑦 2 = 9 7 4 7 9 4 2 . 8 5 𝑆 𝑥 𝑦 3 = 2 8 2 9 4 3 9 7 . 0 4
𝑆 𝑥 𝑦 4 = 1 4 5 2 3 8 8 5 . 5 3 𝑆 𝑥 𝑦 5 = 3 3 9 3 5 9 1 . 7 5 𝑆 𝑥 𝑦 6 = 1 5 8 6 4 5 7 3 . 9 7
𝜌 𝑦 𝑥 1 = 0 . 9 3 6 𝜌 𝑦 𝑥 2 = 0 . 9 9 6 𝜌 𝑦 𝑥 3 = 0 . 9 9 4
𝜌 𝑦 𝑥 4 = 0 . 9 8 3 𝜌 𝑦 𝑥 5 = 0 . 9 8 9 𝜌 𝑦 𝑥 6 = 0 . 9 6 5
𝑤 1 = 0 . 1 3 8 𝑤 2 = 0 . 1 2 7 𝑤 3 = 0 . 1 1 2
𝑤 4 = 0 . 1 8 4 𝑤 5 = 0 . 2 2 2 𝑤 6 = 0 . 2 1 8
𝑆 𝑧 1 = 5 5 5 . 5 8 1 6 𝑆 𝑧 2 = 3 6 5 . 4 5 7 6 𝑆 𝑧 3 = 6 1 2 . 9 5 0 9 2 8 1
𝑆 𝑧 4 = 4 5 8 . 0 2 8 2 𝑆 𝑧 5 = 2 6 0 . 8 5 1 1 𝑆 𝑧 6 = 3 9 7 . 0 4 8 1
𝑍 1 = 4 9 8 . 2 8 𝑍 2 = 3 1 8 . 3 3 𝑍 3 = 4 3 1 . 3 6
𝑍 4 = 3 1 1 . 3 2 𝑍 5 = 2 2 7 . 2 2 𝑍 6 = 3 1 3 . 7 1
𝑆 𝑦 𝑧 1 = 4 8 0 6 8 8 . 2 𝑆 𝑦 𝑧 2 = 2 3 0 0 9 2 . 8 𝑆 𝑦 𝑧 3 = 6 2 3 0 1 9 . 3
𝑆 𝑦 𝑧 4 = 3 6 4 9 4 3 . 4 𝑆 𝑦 𝑧 5 = 1 0 1 5 3 9 . 1 𝑆 𝑦 𝑧 6 = 2 7 7 6 9 6 . 1
𝑆 𝑥 𝑧 1 = 1 5 9 1 4 6 4 8 𝑆 𝑥 𝑧 2 = 5 3 7 9 1 9 0 𝑆 𝑥 𝑧 3 = 1 6 4 9 0 6 7 4 . 5 6
𝑆 𝑥 𝑧 4 = 8 0 4 1 2 5 4 𝑆 𝑥 𝑧 5 = 2 1 4 4 0 5 7 𝑆 𝑥 𝑧 6 = 8 8 5 7 7 2 9
Biases and MSEs of different estimators under comparison based on the above data are given in Table 2.