Expected coverage

Find the expected number of strata covered by ordinary Poisson sampling without stratification. As sequential and ordinary Poisson sampling have the same sample size on average, this gives an approximation for the coverage under sequential Poisson sampling.

This function can also be used to calculate, e.g., the expected number of enterprises covered within a stratum when sampling business establishments.

Usage

expected_coverage(x, n, strata, alpha = 0.001, cutoff = Inf)

Arguments

x

A positive and finite numeric vector of sizes for units in the population (e.g., revenue for drawing a sample of businesses).

n

A positive integer giving the sample size.

strata

A factor, or something that can be coerced into one, giving the strata associated with units in the population. The default is to place all units into a single stratum.

alpha

A numeric vector with values between 0 and 1 for each stratum, ordered according to the levels of strata. Units with inclusion probabilities greater than or equal to 1 - alpha are set to 1 for each stratum. A single value is recycled for all strata. The default is slightly larger than 0.

cutoff

A positive numeric vector of cutoffs for each stratum, ordered according to the levels of strata. Units with x >= cutoff get an inclusion probability of 1 for each stratum. A single value is recycled for all strata. The default does not apply a cutoff.

Value

The expected number of strata covered by the sample design.

See also

prop_allocation() for generating proportional-to-size allocations.

Examples

# Make a population with units of different size
x <- c(rep(1:9, each = 3), 100, 100, 100)

# ... and 10 strata
s <- rep(letters[1:10], each = 3)

# Should get about 7 to 8 strata in a sample on average
expected_coverage(x, 15, s)
#> [1] 7.666667