API Reference

UPmaxentropy(pik::AbstractVector{<:Real})

Maximum entropy sampling (conditional Poisson sampling) implementation.

Samples elements without repetition with fixed sample size, given first-order inclusion probabilities. This method satisfies the maximum entropy criterion among all sampling designs with the same inclusion probabilities.

Arguments

• pik: Vector of first-order inclusion probabilities (0 ≤ pik[i] ≤ 1) The sum of pik determines the sample size.

Returns

• A binary vector indicating selected units (1 = selected, 0 = not selected)

Examples

# Sample with inclusion probabilities summing to 5
pik = [0.2, 0.3, 0.5, 0.8, 0.9, 0.7, 0.6, 1.0]
s = UPmaxentropy(pik)
println("Selected units: ", findall(s .== 1))
println("Sample size: ", sum(s))

References

Tillé, Y. (2006). Sampling Algorithms. Springer.

This code was generated by Claude, based on the UPmaxentropy function from the R package sampling.

UPmaxentropypi2(pik::AbstractVector{<:Real})

Compute second-order inclusion probabilities for maximum entropy sampling.

Arguments

• pik: Vector of first-order inclusion probabilities

Returns

• Matrix of second-order inclusion probabilities π_{kl} = P(k ∈ S, l ∈ S)

rand_multinomial(pik)

Random multinomial draw (for n=1 case). Selects one unit with probabilities proportional to pik.

upme_pik2_from_pikw(pik, w)

Compute second-order inclusion probabilities from first-order probabilities and weights. Uses the formula: π{kl} = (πk * wl - πl * wk) / (wl - w_k) for k ≠ l

upme_pik_from_q(q)

Compute first-order inclusion probabilities from conditional probability matrix q. Used in the iterative algorithm to verify convergence.

pro[i,j] represents the probability that when processing unit i, there are exactly j units remaining to be selected.

upme_piktilde_from_pik(pik, eps=1e-6)

Transform inclusion probabilities through iterative algorithm. This computes adjusted probabilities that ensure the correct first-order inclusion probabilities after the sampling procedure.

upme_q_from_w(w, n)

Compute the matrix of conditional probabilities q[i,z] from weights. q[i,z] represents the probability of selecting unit i given that z units remain to be selected from units i through N.

upme_s_from_q(q)

Generate a sample from the conditional probability matrix q. Sequential sampling: at each step, select unit k with probability q[k,n] where n is the number of units remaining to be selected.