Crate chromy_core 

Chromy’s method of sequential random sampling, as a library.

Chromy (1979) selects units one at a time down an ordered list, each with probability proportional to its size, so that the realised hits of every unit differ from its expected hits by less than one — probability minimum replacement. The procedure is the backbone of many large establishment and household surveys, and of PROC SURVEYSELECT METHOD=PPS_SEQ; until now it lived only inside proprietary software and one Stata module. This crate is the method in the open, with the apparatus that surrounds it in practice:

• pmr: the sequential selection itself, deterministic given the uniforms, with compensated summation and an explicit account of every floating-point adjustment it had to make;
• serpentine and nested: hierarchical sorting of the frame, so that neighbouring units are alike and the systematic character of the selection buys variance;
• mpps: a maximal size measure over several auxiliary variables, for surveys that must serve more than one estimate;
• expected_hits and eqcv: from sizes to expected hits, with certainty units resolved by iteration, and the allocation that equalises anticipated coefficients of variation across variables;
• select / select_from: the full procedure with a random head, as SAS runs it;
• multiplicity_estimate: the estimator that matches the design, with the successive-difference variance;
• joint_inclusion: exact second-order inclusion probabilities for the without-replacement design, by the closed forms of Chauvet and Le Gleut’s Theorem 3 and their randomized-head mixture — the Sen–Yates–Grundy variance becomes exact, not approximated.

The crate has no dependencies and takes its randomness as arguments — a slice of uniforms — so a caller in R, Python or Rust reproduces a selection exactly from its own generator and seed. The reference for every numerical choice is the implementation these functions were distilled from, tested bit for bit in tests/golden.rs.

Chromy, J. R. (1979). Sequential sample selection methods. Proceedings of the American Statistical Association, Survey Research Methods Section, 401–406. Chauvet, G. and Le Gleut, R. (2021). Properties of Chromy’s sampling procedure. Survey Methodology 47(2).

Structs

EqcvAllocation

The outcome of an eqcv search.

EqcvOptions

How eqcv is to search.

Estimate

The totals and their successive-difference variance.

Selected

The outcome of a full selection.

Selection

The outcome of a pmr selection.

Enums

Error

Why a procedure refused to run, or could not finish.

Head

Which units may be drawn as the head of the list.

Key

One sort key: a column of the frame.

Functions

eligible_positions

The list positions eligible to be the head, in list order.

eqcv

Search for the sample-size factors that equalise anticipated CVs.

expected_hits

Expected hits proportional to size.

head_position

Draw a position by cumulative inversion: the first weight whose running sum exceeds u times the total.

joint_inclusion

Joint inclusion probabilities of chosen units, exactly.

mpps

The maximal size measure over several auxiliary variables.

multiplicity_estimate

The multiplicity estimator with successive-difference variance.

nested

The nested sort: plain lexicographic order over the keys.

pmr

Select with probability minimum replacement down a list.

required_uniforms

How many uniforms select_from will consume, beyond the head.

select

Select with the head drawn here, by cumulative inversion.

select_from

Select with the head already drawn.

serpentine

The hierarchical serpentine sort.