Partial Ranked Set Sampling Design. By Abdul Haq Ph.D. Student, Department of Mathematics and Statistics, University of Canterbury, Christchurch, NZ. Outline. Simple random sampling. Ranked set sampling. Examples. Partial ranked set sampling. Simulation and case study. Main findings.
Department of Mathematics and Statistics,
University of Canterbury, Christchurch, NZ.
1. Select randomly units from population.
2.Get careful measurements of selected plants.
3. Estimate population mean and variance based on this sample.
A simple random sample of size
A simple random sample of size is drawn with replacement from the population having mean and variance say , then the sample mean is
1. is an unbiased estimator of i.e. .
Second set of units
Third set of units
Now apply the RSS procedure to these 3 sets of 2 cycles.
Here is a ranked set sample of size
For each measured unit, we need units.
All measured units are independent.
If ranking procedure is uniform for all cycles, then measurements from the same judgment class are i.i.d. but the selected units within each cycle are independent but NOT identically distributed.
Step 1: Define a coefficient such that , where 0 .
Step 2: firstly select simple random samples each of size one.
Step 3: For remaining units, identify sets each of size . Apply RSS on these sets.
Step 4: Above steps can be repeated times for large samples.
PRSS represents PRSS design.
Study variable : Height of trees (ft).
Auxiliary variable : Diameter of trees at chest level (cm).
Correlation coefficient 0.908
See Platt et al. (1988).