Draw n units with probability proportional to size, and estimate

The "lottery" or cumulative-total method, drawing WITH replacement, so the same unit can legitimately appear twice. Selection uses a pinned Lehmer generator so the two language arms draw the SAME units. Indices are one-based.

Usage

Ppssamp(z, y, n, seed = 1)

Arguments

z

Size measure of every unit, strictly positive.

y

Value of the variable of interest for every unit.

n

Number of draws (with replacement), n >= 2.

seed

Seed for the pinned generator.

Value

List with index, p, estimate, se, true_total, n, N.

Details

Formula: p_i = z_i / sum_j z_j; Yhat = (1/n) sum_i y_i / p_i; v(Yhat) = sum_i (y_i/p_i - Yhat)^2 / (n (n - 1))

References

Cochran (1977), Sampling Techniques, 3rd edition, Chapter 9A. Chapter 9A was NOT in the scanned excerpt available to this batch, so the standard published form (Hansen & Hurwitz 1943, Annals of Mathematical Statistics 14(4), 333-362) is used.

Examples

Ppssamp(z = c(1, 2, 3, 4, 5, 6, 7, 8), y = c(1, 2, 3, 4, 5, 6, 7, 8), n = 5L)
#> $index
#> [1] 1 3 7 8 8
#> 
#> $p
#> [1] 0.02777778 0.05555556 0.08333333 0.11111111 0.13888889 0.16666667 0.19444444
#> [8] 0.22222222
#> 
#> $estimate
#> [1] 36
#> 
#> $se
#> [1] 0
#> 
#> $true_total
#> [1] 36
#> 
#> $n
#> [1] 5
#> 
#> $N
#> [1] 8
#> 
#> $method
#> [1] "PPS with replacement, Hansen-Hurwitz estimator"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"