OrderSample

OrderSample(pi, prn=None, *, shape=1.0, sort_method='partial')

Order sampling with fixed distribution shape.

Parameters

pi : InclusionProb

Inclusion probabilities for units in the population.

prn : ArrayLike = None

Permanent random numbers. Should be a flat array of values, the same length as pi, distributed uniform between 0 and 1. The default draws a sample without permanent random numbers.

shape : float = 1.0

Shape parameter for the generalized Pareto distribution that is used as the fixed order distribution shape. The default is sequential Poisson sampling. Setting shape=0 gives Successive sampling and shape=-1 gives Pareto order sampling.

sort_method : (partial, stable) = 'partial'

Sorting method to use for drawing the sample. The default uses a partial sort. Use ‘stable’ if ties should resolve in order.

Attributes

units : Array

Indices for units in the sample.

weights : Array

Design weights for units in the sample.

take_all : Array

Take-all units in the sample.

take_some : Array

Take-some units in the sample.

prn : Array

Random numbers used for drawing the sample.

References

Matei, A., and Tillé, Y. (2007). Computational aspects of order πps sampling schemes. Computational Statistics & Data Analysis, 51: 3703-3717.

Ohlsson, E. (1998). Sequential Poisson Sampling. Journal of Official Statistics, 14(2): 149-162.

Rosén, B. (1997). On sampling with probability proportional to size. Journal of Statistical Planning and Inference, 62(2): 159-191.

Examples

import numpy as np
import pysps

x = np.arange(10)
pi = pysps.InclusionProb(x, 6)

# Draw a sequential Poisson sample using permanent random numbers.

prn = np.random.default_rng(54321).uniform(size=10)
sample = pysps.OrderSample(pi, prn)
sample.units

array([3, 4, 5, 7, 8, 9])

# Get the design weights.

sample.weights

array([2.33333333, 1.75      , 1.4       , 1.        , 1.        ,
       1.        ])

# Units 0 to 2 are take-some units...

sample.take_some

array([0, 1, 2])

# ... and units 3 to 5 are take-all units.

sample.take_all

array([3, 4, 5])

# Draw a Pareto order sample using the same permanent random numbers.

pysps.OrderSample(pi, prn, shape=-1).units

array([3, 5, 6, 7, 8, 9])